Other Cloth Limited (OCL) makes and supplies two products to retailers around the world. Two of the products – the “cloak” and “robe” – require the same resources but in different quantities. Given below are details of the forecast revenues and costs as well as planned resource requirements for the two products.

Product

Cloak

Robe

Selling Price (£)

Resource usage:

Direct Materials (£50 per sq. meter) Direct Labour (£30 per hour) Variable machine cost (£15 per hour) Fixed Costs*

Profit

70

120

Resource per unit

Cost per Quantity cloak per cloak

Cost per robe

Quantity per robe

£50 £30 £15

£ 20 12 5 11.50 21.50

£ 0.40 30 0.40 20 0.33 15

22.50

32.50

0.60 0.67 1.00

The company’s budget has already been prepared. This was based on the production and sales of 40,000 “cloaks” and 52,500 “robes”.

In response to rumors of potential shortages in resources, the company is reviewing its operational plans to determine the most profitable course of action.
The following resource constraints are expected:

*Fixed costs are based on meeting the budget.

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Direct materials Direct labour Machine

Maximum available

50,000 square meters 60,000 hours 50,000 hours

Required:

(a) Based on the currently planned production quantities and selling prices, advise OCL (presenting suitable calculations) on the most profitable product mix (with limited resources). (50% of marks)

(b) Briefly explain “Linear Programming” and state what assumptions are included with respect to the accounting data used to calculate it. (20% of marks)

(c) Management decides to reduce the selling price to Cloaks £60, and Robes £105. This is expected to increase the demand for each product by 15%. State the constraints and objective function that would enable a solution with the reduced selling price and increased demand (using Linear Programming). Note: You are not required to solve or draw the graph.