Jerry Wolfe has a 100-acre farm that he is dividing into one-acre plots, on each of which he builds a house. He then sells the house and land. It costs him $20,000 to build a modest house and $40,000 to build a deluxe house. He has $2,600,000 to cover these costs. The profits are $25,000 for a modest house and $60,000 for a deluxe house. How many of each type of house should he build to maximize profit? How, if at all, do the maximum profit and optimal production policy change if Wolfe is required to build at least 20 of each type of house?

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Asked Oct 1, 2019
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Jerry Wolfe has a 100-acre farm that he is dividing into one-acre plots, on each of which he builds a house. He then sells the house and land. It costs him $20,000 to build a modest house and $40,000 to build a deluxe house. He has $2,600,000 to cover these costs. The profits are $25,000 for a modest house and $60,000 for a deluxe house. How many of each type of house should he build to maximize profit? How, if at all, do the maximum profit and optimal production policy change if Wolfe is required to build at least 20 of each type of house?

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Step 1

To convert the given word problem into a linear programming problem and solve for the optimum values

Step 2

Let x, y represent the number of modest and deluxe houses respectively. The inequalities governing x and y are first formulated.

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constraint s x, y20,x, y integers x+y100 20000x+40000 y < 2600000; or x+2y 130 (I) (2)

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Step 3

The optimization consists in finding x and y satisfying the constraints...

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constra int s r,y20,x, y int egers x+y <100 (1) x+2y130 (2) To max imize P(x, y) 25000x +60000y

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Math

Algebra