A chemical manufacturer produces two products, chemical X and chemical Y. Each product is manufactured by a two-step process that involves blending and mixing in machine A and packaging on machine B. Chemical X provides a $60/unit contribution to profit, while Chemical Y provides a $55 contribution to profit. The processing times for the two products on the mixing machine (A) and the packaging machine (B) are as follows:

product machine A machine B

chemical x 3. 3

chemical y 5. 2

For the upcoming two-week period, machine A has available 90 hours, and machine B has available 60 hours of processing time. Forecasts of the markets indicate that the manufacturer can expect to sell a maximum of 16 units of chemical X and 18 units of chemical Y.

What are the decision variables in this problem?

Write out an algebraic expression for the objective function in this problem.