Asked by T

A farmers’ market manager needs to purchase pints of blueberries and pints of strawberries. His display for berries can hold no more than 50 pints. His customers by no more than 25 pints of blueberries and no more than 40 pints of strawberries. He is able to sell blueberries for $3 per pint and strawberries for $5 per pint. Below is the graph of constraints. Let X represent blueberries and Y represent strawberries.

0. What is the name of the shaded region in the graph?
0. What are the vertices?
0. What is the object function?
0. What is the optimal value of profit?
0. How many pints of blueberries and strawberries should the manager purchase in order to optimize his profit?
Answered by T
Also, I'm not sure how to solve, so if you could go through this step by step that would be great. Thank you :)
Answered by oobleck
he wants to maximize revenue (or profit, since his costs are apparently zero).
So, if he sells b pints of blueberries
and s pints of strawberries
he wants to maximize
p = 3b+5s
subject to the constraints
b+s <= 50
0 <= b <= 25
0 <= s <= 40
I'm sure you can graph those lines. Now just find the points where they intersect, and those are the vertices.
Answered by T
Okay, thank you so much
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