A small drugstore orders copies of a certain magazine ... Your question has expi
ID: 3208875 • Letter: A
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A small drugstore orders copies of a certain magazine ... Your question has expired and been refunded. We were unable to find a Chegg Expert to answer your question. Question: A small drugstore orders copies of a certain magaz... Bookmark A small drugstore orders copies of a certain magazine for its magazine rack each week. Let X equal the number of copies of the magazine that could be sold in a randomly selected week (i.e., X is the demand for the magazine). Suppose X has the mass function given in Exercise 35. Suppose that the store owner pays $1.50 for each magazine and sells the magazines for $2.70 each. Any unsold magazines at the end of the week must be recycled and generate no profit. Suppose that the store owner will order k magazines next week, where k is some constant. (a) (3 points) Express the profit P as a function of k and X. Note that P is a random variable because it is a function of X. (Also note: P is not simply 2.7X 1.5k; your answer should involve the expression min(k, X).) (b) (5 points) For each value of k, let f(k) equal the expected profit. Find f(k) for k = 1, · · · , 6 and express your answer in the form of a table. (c) (2 points) How many magazines should the store owner purchase if the goal is to maximize expected profit?
A small market orders copies of a certain magazine for its magazine rack each week. Let X demand for the magazine, with pmf 15 15 15 15Explanation / Answer
In the question, X equal the number of copies of the magazine that could be sold i.e. the demand for the magazine
Number of magazine in the store is k.
Then, define a new random variable Z = min(X,k) equal the number of magazines actually sold that means Z can be equal to demand or number of magazine which is minimum.
(a) The profit is sell - purchase
$2.70*min(X,k) - $1.50*k
$2.70*Z - $1.50*k
(b) For k = 6, that means number of magazine is equal to demand. So, the probability is
For k = 5
For k=4
For k =3
For k=2
For k=1,
Them we find the expected profit is calculate is $2.70*Z - $1.50*k
(c) 4 magazines should the store owner purchase if the goal is to maximize expected profit.
k 1 2 3 4 5 6 E(Z=6) P(k) 1/15 2/15 3/15 4/15 3/15 2/15 3.80