A meat packer processes cattle and pigs for market, both of which require three operations: preparation, butchering, and packing. For each type of livestock, the profit contribution in dollars per unit processed and the time required for the various operations in hours per unit processed are:

Under its current labor union contract, the packer has available 3,300 hours of preparation time, 2,500 hours of butchering time, and 1,500 hours of packing time over the coming month. Over the same period, the packer can also hire up to 1,500 hours of additional non-union labor at $15 per hour and employ it in any of the three operations. The packer must determine the number of cattle and pigs to process over the coming month so as to maximize profit.

a) Formulate the packers profit maximization problem. Be sure to clearly specify the decision variables, objective function, and constraints.

b) Solve the packers profit maximization problem in Excel. What is the packers optimal production plan and maximum profit?

c) The labor union is willing to provide an additional 100 hours of labor for the following month at $30 per hour, to be used in any of the three operations as to be determined by the packer. The CEO of the meat packing firm turns to you and another junior member of the management team, a graduate, seeking advice. The grad says, no, we should decline the unions offer because $30 per hour is more than the $15 per hour we pay non-union workers. What is your advice?

Product Preparation Butchering Packing Cattle 0.6 0.8 0.3 Pigs 0.5 0.2 0.3 Profit $50 $25 Product Preparation Butchering Packing Cattle 0.6 0.8 0.3 Pigs 0.5 0.2 0.3 Profit $50 $25