# calculus

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A publisher prints and sells both hardcover and paperback copies of the same book. Two machines M and N are needed to manufacture these books. To produce one hardcover copy,machine M works 1/6 hours and N works 1/12 hours. For a paperback copy M and N work 1/15 and 1/16 hours respectively. Each machine maybe operated no more than 12 hours per day. If the profit is R12 on a hardcover copy and R8 on a paperback copy, how many of each type should be made per day to maximize the profit?

• calculus -

maximize p=12x+8y subject to
x/6 + y/15 <= 12
x/12 + y/16 <= 12
x >= 0
y >= 0

I get (x,y) = (0,180) for p=1440

better check; seems odd not to make any hardbacks

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