(Solved Homework): Ctrt ell is the new owner of Coffee Country Roasters. They roast and blend nomy coffee to sell…

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Ctrt ell is the new owner of Coffee Country Roasters. They roast and blend nomy coffee to sell on the internet. Their best sellers are “Best Blend” and” Blend” coffee. Both are blended from three basic grades of coffee: Best blend: 50% grade A, 20% grade B, and 3096 grade C Economy: 2096 grade A, 50% grade B, and 30% grade C The market prices are $790/ton for Best and $700/ton for Economy. The firm is given the option of buying up to 100 tons of grade A at $800/ton, 100 tons of grade B at $600/ton, and 75 tons of grade C at $400/ton. The profit on the Best Blend is $150 per ton and the profit on the Economy Blend is $120 per ton. Jessica would like to maximize her profit. a. Formulate this problem as a linear program.

Expert Answer

Answer

Suppose X quantity of Best Blend is produced

And Y quantity of Economy Blend is produced.

Therefore the respective grades will be

X = 0.5X + 0.2X + 0.3X

Y = 0.2Y + 0.5Y + 0.3Y

Thus, linear equations will be,

0.5X + 0.2Y <= 100

0.2X + 0.5Y <=100

0.3X + 0.3Y <= 75

Objective function is Maximize Z =150X + 120Y

Now one by one we put in the points in the objective function. Therefore point (166.667, 83.334) gives maximum value of Z. Z= 35000

When Z= 150X + 110Y, at (166.667, 83.334) value of Z= 34166

When only 80 tons of grade B is available,

0.5X + 0.2Y <= 100

0.2X + 0.5Y <=80

0.3X + 0.3Y <= 75

Still Z maximum = 35000 at (166.67,83.33)

No i will not purchase 12 tons of grade C at $3000

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