SOLUTION: A backpack manufacturer produces an internal frame pack and an external frame pack. Let X represent the number of internal frame packs produced in one hour and let Y represent the

Algebra ->  Human-and-algebraic-language -> SOLUTION: A backpack manufacturer produces an internal frame pack and an external frame pack. Let X represent the number of internal frame packs produced in one hour and let Y represent the       Log On


   

Question 318406: A backpack manufacturer produces an internal frame pack and an external frame pack. Let X represent the number of internal frame packs produced in one hour and let Y represent the number of external frame packs produced in one hour. Then the inequalities X+3<18, 2x+y<16 , x>0 , and y>0 describe the constraints for manufacturing both packs. Use the profit function f(X)=50x+80y and the constraints given to determine the maximum profit for manufacturing both backpacks for the given constraints.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B3%3C18
x%3C15
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2x%2By%3C16
y%3C-2x%2B16
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x%3E0
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y%3E0
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As you can see the constraint, x%2B3%3C18 doesn't even enter into calculating the feasible region because the constraint, 2x%2By%3C16 really identifies the region.
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Check the value of the function at the three vertices:
(0,0):f=50x%2B80y=50%280%29%2B80%280%29=0
(8,0):f=50x%2B80y=50%288%29%2B80%280%29=400
(0,16):f=50x%2B80y=50%280%29%2B80%2816%29=1280
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The maximum, 1280, occurs at (0,16).