Refer to the data given in the preceding exercise for Plato Corporation. Assume that the direct-labor rate is $12 per hour, and 11,000 labor hours are available per year. In addition, the company has a short supply of machine time. Only 9,000 hours are available each year. Alpha requires one machine hour per unit, and Beta requires two machine hours per unit.

Required:
Formulate the production planning problem as a linear program. Specifically identify
(1) The decision variables,
(2) The objective function, and
(3) The constraints.