PTP produces two products from different combinations of the same resources. Details of the selling price and costs per unit for each product are shown below:

The fixed costs of the company are $50 000 per month. PTP aims to maximize profits from production and sales. The production plan for June is currently under consideration.The following resources are available in June:Material A .....................4800kgMaterial B .....................3900kgLabour ...........................2500 hoursMachine hours .............5000 hour

Required:(a) (i) Identify the objective function and the constraints to be used in a linear programming model to determine the optimum production plan for June.The solution to the linear programming model shows that the only binding constraints in June are those for Material A and Material B.(ii) Produce, using simultaneous equations, the optimum production plan and resulting profit for June. (You are NOT required to draw or sketch a graph.)Based on the optimal production plan for June, the management accountant at PTP has determined that the shadow price for Material A is $7 per kg.(b) Explain the meaning of the shadow price for Material A.

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Product E Product M Selling price Material A ($12 per kg) 175 125 60 24 Material B ($5 per kg) Labour ($20 per hour) 10 15 20 40 Variable overhead 14 28 ($7 per machine hour)