Question

Canan Farms processes milk into butter and cheese. The firm has 72 hours of processing time available each week for each process. The production time required and the profit contribution of each product are the following:

Product Production time (hours/ton processed) Profit/ton

	Process 1	Process 2	Process 3
Butter	1.85	3.50	1.00	$2500
Cheese	2.45	2.25	0.00	$1800

In formulating a linear optimization model to maximize profit, the decision variable should be:

A. the number of tons of butter and cheese to produce

B. the number of tons processed in each of the three processes

C. the production time used in each process to make butter and cheese

Answer 1

Ans. A is the option. It is said that 72 hrs is available for each process per week. Hence, if x is tons of butter produced and y is tons of cheese produced, then for process 1 the total time would be 1.85x + 2.45y <=72 and so on for other processes. Hence the decision variables would be the number of tons of butter and cheese to produce.