Linear programming. (CMA, adapted) Cape Breton Manufacturing Ltd. (CBML) produces two products, Smart and Supersmart. The company has a just-in-time (JIT) inventory policy, therefore the direct materials, work-in-process, and finished goods inventories are not mate- rially different from $0. Careful planning and production schedules are needed to ensure the success of this JIT policy. In the coming month, the sales manager estimates that the maximum demand will be 2,500 units of Smart and 2,000 units of Supersmart. CBML's con- tract with its supplier of direct materials states that in the coming month it will deliver a maximum of 38,000 kilograms at $1.25/kg. Employee vacations will limit direct labour to 900 hours in the coming month and the direct labour wage is $20/hour. Price and production data available are:

REQUIRED 1. Formulate and solve the linear programming problem to determine the production mix that will maximize the total contribution margin in the coming month for CBML.
2. Calculate the overtime premium CBML should be willing to pay per hour to increase its direct labour capacity by an added 50 hours in the coming month.LO1

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Smart Supersmart Selling price per unit $30.00 $32.00 Direct materials (kg) for each unit 10.00 8.00 Direct labour (minutes) for each unit 12.00 18.00 Variable overhead (direct labour-hours) 7.00 8.50