The Chris Beehner Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc; the company has available a total of 25,000 lb of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 lb of steel and 20 lb of zinc, and each yields a profit of $90. Each model B gate requires 100 lb of steel and 30 lb of zinc and can be sold for a profit of $70. Find the optimal solution?

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Business

Lacey

5 March, 21:34

The Chris Beehner Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc; the company has available a total of 25,000 lb of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 lb of steel and 20 lb of zinc, and each yields a profit of $90. Each model B gate requires 100 lb of steel and 30 lb of zinc and can be sold for a profit of $70. Find the optimal solution?

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Jaylyn Woodward · Answer 1

producing 200 units of Model A would be the best of the 25,000 lbs of steel and 4,000 zinc available

With a profit of 200 units x $90 each = 18,000 dollars

Explanation:

Model A contribution:

90 / 125 = 0.72

90 / 20 = 4.5

Model B contribution:

70 / 100 = 0.7

70 / 30 = 2.33

As model B generates lower contribution for both scarse resources is not convinient to produced altogether.

It should produce Model A as much as it can and only fill with Model B if needed

25,000 lbs of steel / 125 per Model A = 200 units of A

200 units of A x 20 lbs of zinc each = 4,000 lbs of zinc

producing 200 units of Model A would be the best of the 25,000 lbs of steel and 4,000 zinc available