How do I get the profit equation? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)On a zero-sum game betting marketPredicting profit with price variationHow would I solve for long run average profit?What are the expected value and the standard deviation of the net profit made by the pharmacist on this medicine in any given month?Comprehensive conditional probability questionHelp for understanding this random variable derivationAm I on the right track? - long run profit problemNeed help to find a formula for math problem for anticipation of event according to several variablesWhat is the probability that the stock trader gains money if the price of a share goes up or down with the probability of 50% each day?How do I further expand the conditional probability?
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How do I get the profit equation?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)On a zero-sum game betting marketPredicting profit with price variationHow would I solve for long run average profit?What are the expected value and the standard deviation of the net profit made by the pharmacist on this medicine in any given month?Comprehensive conditional probability questionHelp for understanding this random variable derivationAm I on the right track? - long run profit problemNeed help to find a formula for math problem for anticipation of event according to several variablesWhat is the probability that the stock trader gains money if the price of a share goes up or down with the probability of 50% each day?How do I further expand the conditional probability?
$begingroup$
- A retail store is currently short of a certain product, and the manager is now planning on how many amounts of such product to import for the sales of them in next month. The store pays $$20$ (the import price) per unit of the product, and then sells it for $$30$ (the marked price in that store) per unit. However, if the store is not able to sell these imported products in the next month, these products must be disposed and can not be sold afterwards. Therefore, there is a trade-off between maximizing the profits (the total amount of money gained by selling the products minus the total amount of money paid to import the products) and minimizing the risk of overstock (which will then result in wasting $$20$ per unit of the unsold products). Suppose that the demand for such products in a randomly chosen month has the Binomial distribution $textBinom(n = 20,p = 0.3).$ Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store.
(a) Let $A$ (a non-negative integer) denote the amount of such products that the manager imports, and let $B$ (a non-negative integer) denote the demand of such products. Write down the expression of the profit (in dollars) that the store can make in next month, which should involve $A$ and $B.$
(b) Let $A$ (a non-negative integer that is not greater than $20$) denote the amount of such products that the manager imports. Find the expression of the conditional probability that the demand of such products is $k,$ given that the demand does not exceed $A.$ You may assume here that $k$ is some non-negative integer that is not greater than $A.$ Your answer should involve $A$ and $k.$
(c) Suppose the manager finally decides to import A units of such products (you may assume that $A leq 20$), find the expected profit that the retail store can make for selling these products in next month. Your answer should involve $A.$
For a) I have profit = $30B-20A$
however, am not sure how to include this fact: Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store
also for c) I'm having troubles computing the E(profit) any help?
probability statistics
asked Mar 27 at 17:49
RitaRita
64
$endgroup$
add a comment |
$begingroup$
- A retail store is currently short of a certain product, and the manager is now planning on how many amounts of such product to import for the sales of them in next month. The store pays $$20$ (the import price) per unit of the product, and then sells it for $$30$ (the marked price in that store) per unit. However, if the store is not able to sell these imported products in the next month, these products must be disposed and can not be sold afterwards. Therefore, there is a trade-off between maximizing the profits (the total amount of money gained by selling the products minus the total amount of money paid to import the products) and minimizing the risk of overstock (which will then result in wasting $$20$ per unit of the unsold products). Suppose that the demand for such products in a randomly chosen month has the Binomial distribution $textBinom(n = 20,p = 0.3).$ Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store.
(a) Let $A$ (a non-negative integer) denote the amount of such products that the manager imports, and let $B$ (a non-negative integer) denote the demand of such products. Write down the expression of the profit (in dollars) that the store can make in next month, which should involve $A$ and $B.$
(b) Let $A$ (a non-negative integer that is not greater than $20$) denote the amount of such products that the manager imports. Find the expression of the conditional probability that the demand of such products is $k,$ given that the demand does not exceed $A.$ You may assume here that $k$ is some non-negative integer that is not greater than $A.$ Your answer should involve $A$ and $k.$
(c) Suppose the manager finally decides to import A units of such products (you may assume that $A leq 20$), find the expected profit that the retail store can make for selling these products in next month. Your answer should involve $A.$
For a) I have profit = $30B-20A$
however, am not sure how to include this fact: Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store
also for c) I'm having troubles computing the E(profit) any help?
probability statistics
asked Mar 27 at 17:49
RitaRita
64
$endgroup$
$begingroup$
Do you know the general expression for the expected value of a quantity?
$endgroup$
– Ertxiem
Mar 28 at 0:07
add a comment |
$begingroup$
- A retail store is currently short of a certain product, and the manager is now planning on how many amounts of such product to import for the sales of them in next month. The store pays $$20$ (the import price) per unit of the product, and then sells it for $$30$ (the marked price in that store) per unit. However, if the store is not able to sell these imported products in the next month, these products must be disposed and can not be sold afterwards. Therefore, there is a trade-off between maximizing the profits (the total amount of money gained by selling the products minus the total amount of money paid to import the products) and minimizing the risk of overstock (which will then result in wasting $$20$ per unit of the unsold products). Suppose that the demand for such products in a randomly chosen month has the Binomial distribution $textBinom(n = 20,p = 0.3).$ Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store.
(a) Let $A$ (a non-negative integer) denote the amount of such products that the manager imports, and let $B$ (a non-negative integer) denote the demand of such products. Write down the expression of the profit (in dollars) that the store can make in next month, which should involve $A$ and $B.$
(b) Let $A$ (a non-negative integer that is not greater than $20$) denote the amount of such products that the manager imports. Find the expression of the conditional probability that the demand of such products is $k,$ given that the demand does not exceed $A.$ You may assume here that $k$ is some non-negative integer that is not greater than $A.$ Your answer should involve $A$ and $k.$
(c) Suppose the manager finally decides to import A units of such products (you may assume that $A leq 20$), find the expected profit that the retail store can make for selling these products in next month. Your answer should involve $A.$
For a) I have profit = $30B-20A$
however, am not sure how to include this fact: Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store
also for c) I'm having troubles computing the E(profit) any help?
probability statistics
asked Mar 27 at 17:49
RitaRita
64
$endgroup$
- A retail store is currently short of a certain product, and the manager is now planning on how many amounts of such product to import for the sales of them in next month. The store pays $$20$ (the import price) per unit of the product, and then sells it for $$30$ (the marked price in that store) per unit. However, if the store is not able to sell these imported products in the next month, these products must be disposed and can not be sold afterwards. Therefore, there is a trade-off between maximizing the profits (the total amount of money gained by selling the products minus the total amount of money paid to import the products) and minimizing the risk of overstock (which will then result in wasting $$20$ per unit of the unsold products). Suppose that the demand for such products in a randomly chosen month has the Binomial distribution $textBinom(n = 20,p = 0.3).$ Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store.
(a) Let $A$ (a non-negative integer) denote the amount of such products that the manager imports, and let $B$ (a non-negative integer) denote the demand of such products. Write down the expression of the profit (in dollars) that the store can make in next month, which should involve $A$ and $B.$
(b) Let $A$ (a non-negative integer that is not greater than $20$) denote the amount of such products that the manager imports. Find the expression of the conditional probability that the demand of such products is $k,$ given that the demand does not exceed $A.$ You may assume here that $k$ is some non-negative integer that is not greater than $A.$ Your answer should involve $A$ and $k.$
(c) Suppose the manager finally decides to import A units of such products (you may assume that $A leq 20$), find the expected profit that the retail store can make for selling these products in next month. Your answer should involve $A.$
For a) I have profit = $30B-20A$
however, am not sure how to include this fact: Note that it is possible that the demand exceeds the amounts of the products in the store, in which case the store can only sell all the amount of the products in the store
also for c) I'm having troubles computing the E(profit) any help?
probability statistics
probability statistics
asked Mar 27 at 17:49
RitaRita
64
asked Mar 27 at 17:49
RitaRita
64
edited Mar 27 at 18:09
Rita
asked Mar 27 at 17:49
RitaRita
64
asked Mar 27 at 17:49
RitaRita
64
asked Mar 27 at 17:49
RitaRita
64
64
$begingroup$
Do you know the general expression for the expected value of a quantity?
$endgroup$
– Ertxiem
Mar 28 at 0:07
add a comment |
$begingroup$
Do you know the general expression for the expected value of a quantity?
$endgroup$
– Ertxiem
Mar 28 at 0:07
$begingroup$
Do you know the general expression for the expected value of a quantity?
$endgroup$
– Ertxiem
Mar 28 at 0:07
$begingroup$
Do you know the general expression for the expected value of a quantity?
$endgroup$
– Ertxiem
Mar 28 at 0:07
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The store sells $B$ or $A$ items, whichever is less. The way to indicate this is $min(A,B).$ ("Min" stands for "minimum.") The profit is $$30min(A,B)-20A.$$
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
$endgroup$
add a comment |
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$begingroup$
The store sells $B$ or $A$ items, whichever is less. The way to indicate this is $min(A,B).$ ("Min" stands for "minimum.") The profit is $$30min(A,B)-20A.$$
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
$endgroup$
add a comment |
$begingroup$
The store sells $B$ or $A$ items, whichever is less. The way to indicate this is $min(A,B).$ ("Min" stands for "minimum.") The profit is $$30min(A,B)-20A.$$
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
$endgroup$
add a comment |
$begingroup$
The store sells $B$ or $A$ items, whichever is less. The way to indicate this is $min(A,B).$ ("Min" stands for "minimum.") The profit is $$30min(A,B)-20A.$$
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
$endgroup$
The store sells $B$ or $A$ items, whichever is less. The way to indicate this is $min(A,B).$ ("Min" stands for "minimum.") The profit is $$30min(A,B)-20A.$$
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
answered Mar 27 at 18:03
saulspatzsaulspatz
17.6k31536
17.6k31536
add a comment |
add a comment |
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Do you know the general expression for the expected value of a quantity?
$endgroup$
– Ertxiem
Mar 28 at 0:07