MarTay Productions Inc. manufactures two products, X and Y. The company utilizes just-in-time inventory techniques whereby little or no raw materials, work-in-process or finished goods inventories are maintained. Careful planning of production schedules is required to ensure the success of the just-in-time inventory systems.

For the month of April, the sales manager estimates that the maximum demand will be 2,500 units of product X and 2,000 units of product Y. The company's contract with its raw materials supplier stipulates that a maximum of 32,000 kilograms of direct materials will be delivered to MarTay Productions Inc. during April at a cost of $1.25 per kilogram. Employee vacations are expected to limit direct labour to 900 hours during April at a rate of $20.00 per hour.

Price and production data for each product are as follows:

X Y

Selling Price $30.00 per unit $32.00 per unit

Raw materials 10 kg per unit 8 kg per unit

Direct labour 12 minutes per unit 18 minutes per unit

Variable overhead $7.00 per DLH $8.50 per DLH

Required:

Formulate the linear programming problem required to determine the production mix plan that will maximize the total contribution margin during the month of April.

Explain step by step how and where you got the figures from.