Formulate and Solve Linear Program: The Elon Company manufactures two industrial productsX-IO, which sells for $90 a
Question:
Formulate and Solve Linear Program: The Elon Company manufactures two industrial products—X-IO, which sells for $90 a unit, and Y-I2, which sells for $85 a unit. Each product is processed through both of the company's manufacturing departments. The limited availability of labor, material, and equipment capacity has restricted the ability of the firm to meet the demand for its products. The production department believes that linear programming can be used to routinize the production schedule for the two products. The following data are available to the production department:
The overhead costs for Elon are accumulated on a plantwide basis. The overhead is assigned to products on the basis of the number of direct labor-hours required to manufacture the product. This base is appropriate for overhead assignment because most of the variable overhead costs vary as a function of labor time. The estimated overhead cost per direct labor-hour is:
The production department formulated the following equations for the linear programming statement of the problem.
A = Number of units of X-10 to be produced
B = Number of units of Y-12 to be produced Objective function to minimize costs:
Minimize 85A + 62B Constraints: Material:
Required:
a. The formulation of the linear programming equations as prepared by Elon Company's production department is incorrect. Explain what errors have been made in the formulation prepared by the production department.
b. Formulate and label the proper equations for the linear programming statement of Elon Company's production problem.
c. (Computer required.) Solve the linear program and determine the increase in the price of direct materials that would be required to change the product mix from that obtained in the optimal solution.
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