SOLUTION: An art store sells framed photographs and prints. It buys the photos and prints from a supplier, but it makes its own frames. Each photograph costs the store $20 and requires 2 hou

Question 473256: An art store sells framed photographs and prints. It buys the photos and prints from a supplier, but it makes its own frames. Each photograph costs the store $20 and requires 2 hours of framing time. Each print costs the store $25 and requires five hours for framing. The store has $400 to spend and 60 hours of framing time. It makes a profit of $20 on each framed photo and a profit of $40 on each frame print. How many photos & prints should the store buy to maximize its profit? thank you very much for your help please till me where to find your solution.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An art store sells framed photographs and prints. It buys the photos and prints from a supplier, but it makes its own frames.
Each photograph costs the store $20 and requires 2 hours of framing time.
Each print costs the store $25 and requires five hours for framing.
------------
The store has $400 to spend and 60 hours of framing time.
Equations:
------------
Value: 20h + 25t <= 400
Framing: 2h + 5t <= 60
------------
It makes a profit of $20 on each framed photo and a profit of $40 on each frame print.
Objective Function:
P = 20h + 40t
----------------
h>= 0
t>= 0
---
Graph h <= (-5/4)t+20
and h <= (-5/2)t + 30
---
Find their point of intersection: (t,h) = (8,10)
----

-----
Vertex points: (12,0) ; (8,10) ; (0,20)
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How many photos & prints should the store buy to maximize its profit?
---
Evaluate P = 20h + 40t at each of the vertex points:
(12,0) gives P = 20*12 + 0 = 240
---
(8,10) gives P = 20*8+40*10 = 560
---
(0,20) gives P = 0 + 40*20 = 800
=========================
Max profit comes by making zero photos and 20 prints.
=================
Cheers,
Stan H.
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