A manufacturer of rotary pumps is planning production for the next four months. The forecast demand for the rotary pumps is shown in the following table.
Rotary pump SEP OCT NOV DEC
Standard 650 875 790 1,100
Heavy duty 900 350 1,200 1,300
At the beginning of September, the warehouse is expected to be completely empty. There is room for no more than 1,800 rotary pumps to be stored. Holding costs for both types are $5 per unit per month. Because workers are given time off during the holidays, the manufacturer wants to have at least 800 standard rotary pumps and 850 heavy duty rotary pumps already in the warehouse at the beginning of January.
Production costs are $125 per unit for standard rotary pumps and $135 per unit for heavy duty rotary pumps. Because demand for raw materials is rising, production costs are expected to rise by 5% per month through the end of the year.
Labor to make the standard rotary pump is 0.45 hours per unit; making heavy duty rotary pumps takes 0.52 hours per unit of labor. Management has agreed to schedule at least 1,000 hours per month of labor. As many as 200 extra hours per month are available to management at the same cost, except during the month of December, when only 100 extra hours are possible.
Formulate the given problem scenario as a linear program so as to determine the production schedule for standard and heavy duty rotary pumps for the four months.