Find the number of books of each type that the company should publish to maximize its profits.?

Question

A small publishing company is planning to publish 2 books this month: book A and book B. The publishing cost is $6 each for book A and $8 each for book B. The total cost can be no more than $7,200. The company cannot publish more than 560 copies of book A and 720 copies of book B. The profit per book A is $10, and the profit per book B is $15. Find the number of books of each type that the company should publish to maximize its profits.

Answer 1

240 A
720 B
cost = 7200
profit = 13200

Constraint equations:
6A + 8B ≤ 7200
A ≤ 560
B ≤ 720

Maximize: P = 10A + 15B

You can use the graph and corner point method here.
Corner points are (240,720) and (560,480), and substitution into the profit equation quickly leads to the solution.

Answer 2

constraints:
6A + 8B ≤ 7200
A ≤ 560
B ≤ 720
and profit P = 10A + 15B

feasible region is a rectangle with chopped off top right corner, corners at (0,0), (560,0), (560,480), (240,720), and (0,720). Since most profit comes from book B, publish as many as you can, then the rest A. This leads us to pick (240,720) as the most profitable corner. Testing, 10(240)+15(720) = 13,200. Just to compare, 10(560)+15(480) = 12,800.

Answer 3

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Answer 4

6A + 8B ≤ 7200
A ≤ 560
B ≤ 720

Max: 10A + 15B = R(A, B)

the two boundary points are
(A, B) = (240 , 720) & (560, 480)

R(240 , 720) is clearly the bigger value...


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