A liquor company produces and sells two kinds of liquor: blended whiskey and bourbon. The company purchases intermediate products in bulk, purifies them by repeated distillation, mixes them, and bottles the final product under their own brand names. In the past, the firm has always been able to sell all that it produced. The firm has been limited by its machine capacity and available cash. The bourbon requires 3 machine hours per bottle while, due to additional blending requirements, the blended whiskey requires 4 hours of machine time per bottle. There are 20,000 machine hours available in the current production period. The direct operating costs, which are principally for labor and materials, are $3.00 per bottle of bourbon and $2.00 per bottle of blended whiskey. The working capital available to finance labor and material is $4000; however, 45% of the bourbon sales revenues and 30% of the blended-whiskey sales revenues from production in the current period will be collected during the current period and be available to finance operations. The selling price to the distributor is $6 per bottle of bourbon and $5.40 per bottle of blended whiskey.
a) Formulate a linear program that maximizes contribution subject to limitations on machine capacity and working capital.
b) What is the optimal production mix to schedule?
c) Can the selling prices change without changing the optimal production mix?
d) Suppose that the company could spend $400 to repair some machinery and increase its available machine hours by 2000 hours. Should the investment be made?
e) What interest rate could the company afford to pay to borrow funds to finance its operations during the current period?