Alan Industries is expanding its product line to include new models: Model A, Model B, and Model C. These are to be produced on the same production equipment, and the objective is to meet the demands for the three products using overtime where necessary. The demand forecast for the next four months, in required hours, is PRODUCT APRIL MAY JUNE JULY Model A Model B Model C 800 600 700 600 700 500 800 900 700 1,200 1,100 850 Because the products deteriorate rapidly, there is a high loss in quality and, consequently, a high carryover cost into subsequent periods. Each hour’s production carried into future months costs $3 per productive hour of Model A, $4 for Model B, and $5 for Model C.

Production can take place during either regular working hours or overtime. Regular time is paid at $4 when working on Model A, $5 for Model B, and $6 for Model C. Overtime premium is 50 percent.

The available production capacity for regular time and overtime is APRIL MAY JUNE JULY Regular time Overtime 1,500 $700 1,300 650 1,800 900 1,700 850

a. Set up the problem in matrix form and show appropriate costs.

b. Show a feasible solution.