SOLUTION: After hurricane charley devastated central florida unexpectedly, orlando residents prepared for hurricane frances by boarding up windows and filling up their cars with gas. It took

Question 1030359: After hurricane charley devastated central florida unexpectedly, orlando residents prepared for hurricane frances by boarding up windows and filling up their cars with gas. It took hours of standing in line to get plywood, and lines for gas were just as time-consuming. A student at Seminole Community College decides to do a spoof of the "Got Milk" ads and creates two T-shirts: "Got Plywood," with a line of people in a home improvement store, and "got gas," with a street lined with cars waiting to pump gasoline. The "got plywood" shirt costs $8 to make, and she sells them for $13. The "Got Gas" shirts cost $6 to make, and she sells them for $10. She decides to limit her costs to $1400. She estimates that demand for these T-shirts will not exceed 200 T-shirts. Find the number of each type of T-shirt she would make to yield maximum profit.
I've been struggling with this story problem with what seems like forever. Please help, showing all work.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The "got plywood" shirt costs $8 to make, and she sells them for $13. The "Got Gas" shirts cost $6 to make, and she sells them for $10. She decides to limit her costs to $1400. She estimates that demand for these T-shirts will not exceed 200 T-shirts. Find the number of each type of T-shirt she would make to yield maximum profit.
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Note:: p >= 0 ; g >= 0 so the solution is in QI
Profit:: P = 5p + 4g
Cost:: 6g + 8p <= 1400 so graph g <= (-4/3)p + 233.33
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Demand: g + p <= 200 so graph g <= -p + 200
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Note:: These border lines intersect at (100,100),
Other (p,g) vertices are (0,200) and (175,0)
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Determine max profit using Profit = 5p + 4g
Using (100,100) you get Profit = 500 + 400 = 900
Using (0,200) you get Profit = 5*0 + 4*200 = 800
Using (175,0) you get Profit = 5*175 + 4*0 = 875
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Ans: Max Profit comes from p = 100 and g = 100
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Cheers,
Stan H.
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