Question

Please provide the decision variables, objective function, and constraints. Ideally on paper and not excel.

A small, but exclusive, coffee blender produces three blends of coffee during the holiday season. She produces these blends by mixing four types of coffee beans in various amounts for each particular blend. Although she tries to satisfy the demands of all her customers, she rarely has enough coffee beans to meet this demand. But, she must meet at least 70% of the demand for each blend or she feels that she will lose her most important customers and be forced out of business. The following table lists the amount of each bean that make ups each kg of each blend, the amount of each bean that is available, the demand for each blend, and the profits per kg of each blend. Blend Z 0.2 0.1 Bean A Bean B Bean C Bean D Demand (kg) Profit (per kg) Blend X 0.7 0.1 0.1 0.1 30.0 $10.50 Blend Y 0.3 0.4 0.1 0.6 0.2 47.3 $12.75 Amount available (kg) 40 70 50 25 0.1 65.8 $8.5 How much of each blend should be produced in order to maximize the coffee blender's profits? Formulate this problem as a linear programming model. DO NOT SOLVE.

Answer 1

Objective function refers to the function that is either maximized or minimized. The constraints may be equalities or inequalities. So, in linear programming problems, linear objective functions are minimized or maximized which is subject to linear constraints. Thus, in a linear programming problem the objective function and the constraints must be linear functions of the decision variables.