Dan's Coffee sells two types of coffee blends

Question

Dan's Coffee sells two types of coffee blends: Arabica Blend and Robusta Blend. Arabica Blend is one-half Brazilian beans and one-half Kenyan beans. Robusta Blend is one-quarter Brazilian beans and three-quarters Kenyan beans. Profit on the Arabica Blend is $3.50 per pound, while profit on the Robusta Blend is $4.00 per pound. Each day Dan receives a shipment of 200 pounds of Brazilian beans and 330 pounds of Kenyan beans to use for the two blends. Find the amount of each blend Dan should make each day to maximize profit? What is the maximum profit?

Answer 1

A is the amount of Arabica Blend

R is the amount of Robusta Blend

Objective profit function is 3.5A + 4R

(1/2)A + (1/4)B = 200

(1/2)A + (3/4)B = 330

Multiplies both equations by 4:

2A + B = 800

2A + 3B = 1320

2B = 520

B = 260

(1/2)A + (1/4)(260) = 200

(1/2)A + 65 = 200

(1/2)A = 135

A = 270

270 lbs of Arabica Blend requires 135 lbs of Brazilian beans and 135 lbs of Kenyan beans.

260 lbs of Robusta Blend requires 65 lbs of Brazilian beans and 195 lbs of Kenyan beans.

Totals are 200 lbs of Brazilian beans and 330 lbs of Kenyan beans.

THe profit is 3.5 * 270 + 4 * 260 = $1985