Chapter 12.1, Problem 28E

In Example 2, Pete’s Coffees mixes Colombian beans and Kona beans to make Rich Blend and Hawaiian Blend. It may be that Pete’s could make slight variations in the proportions of Colombian and Kona beans in these two blends without affecting the taste of the coffee. Why would Pete’s consider doing this? What effect would it have on the objective function, the constraints, the region of possible solutions, and the solution to the example?

EXAMPLE 2 SOLVING A LINEAR PROGRAMMING PROBLEM Pete’s Coffees sells two blends of coffee beans, Rich Blend and Hawaiian Blend. Rich Blend is one-half Colombian beans and one-half Kona beans, and Hawaiian Blend is one-quarter Colombian beans and three-quarters Kona beans. Profit on the Rich Blend is $\$2$ per pound, whereas profit on the Hawaiian Blend is $\$3$ per pound. Each day, the shop can obtain $200$ pounds of Colombian beans and $60$ pounds of Kona beans, and it uses that coffee only in the two blends. If the shop can sell all that it makes, how many pounds of Rich Blend and of Hawaiian Blend should Pete’s Coffees prepare each day to maximize profit?