The Tripro Company produces and sells three products hereafter referred to as Products A, B, and C. The company is currently changing its shortrange planning approach in an attempt to incorporate some of the newer planning techniques. The controller and some of his staff have been conferring with a consultant on the feasibility of using a linear programming model for determining the optimum product mix. Information for short-range planning has been developed in the same format as in prior years. This information includes expected sales prices and expected direct labor and material costs for each product. In addition, variable and fixed overhead costs were assumed to be the same for each product because approximately equal quantities of the products were produced and sold.

All three products use the same type of direct material which costs \(\$ 1.50\) per pound of material. Direct labor is paid at the rate of \(\$ 5.00\) per direct labor hour. There are 2,000 direct labor hours and 20,000 pounds of direct materials available in a month.
Required:

(a) Formulate and label the linear programming objective function and constraint functions necessary to maximize Tripro's contribution margin. Use \(Q_{A}, Q_{B}, Q_{c}\) to represent units of the three products.

(b) What underlying assumptions must be satisfied to justify the use of linear programming?

(c) The consultant, upon reviewing the data presented and the linear programming functions developed, performed further analysis of overhead costs. He used a multiple linear regression model to analyze the overhead cost behavior. The regression model incorporated observations from the past 48 months of total overhead costs and the direct labor hours for each product. The following equation was the result:

The total regression has been determined to be statistically significant as has each of the individual regression coefficients.
Reformulate the objective function for Tripro Company using the results of this analysis.

Transcribed Image Text:

Price and Cost Information (Per Unit) A B C Selling price.............. $25.00 $30.00 $40.00 Direct labor................ 7.50 10.00 12.50 Direct materials................ 9.00 6.00 10.50 Variable overhead.............. 6.00 6.00 6.00 Fixed overhead.. 6.00 6.00 6.00