Question

The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees, Inc. is to maximize profits.

1.Write the Linear Programming Model

2.Using Excel Solver to find the optimal solution and the weekly maximum profit? show your spreadsheet model, and both the answer report and the sensitivity report)

3.How much profit of each pound of American blend coffee can change without affecting the optimal solution?

4.Which constraint is a binding one?

Answer 1

Solution:

Linear Programming Model:

Let the American blend be A and British Blend B.

Objective Function :

Maximize Z = 2A + B

as profit for American Blend = $2

profit for British Blend = $1

subject to constraints

0.75A + 0.5B <= 300

0.25A + 0.5 B <= 200

(Ounces are converted to pounds as maximum availability is given in pounds. The formation of equation can be understood from the Spreadsheet)

Therefore ,

Linear Programming Model is :

Objective Function :

Maximize Z = 2A + B

subject to constraints

0.75A + 0.5B <= 300

0.25A + 0.5 B <= 200

Optimal Solution and Weekly maximum profit:

Optimal Solution is produce 400 pounds of American Blend and maximum weekly profit is $800.

Answer Report:

Sensitivity Report:

Binding Constraint

Colombian Beans

0.75A + 0.5B <= 300