LM produces two products from different quantities of the same resources using a just-in-time (JIT) production system. The selling price and resource requirements of each of these two products are as follows:

Fixed overheads are absorbed at the rate of $3 per direct labour hour.Market research shows that the maximum demand for products L and M during December will be 400 units and 700 units respectively.At a recent meeting of the purchasing and production managers to discuss the company?s production plans for December, the following resource availability for December was identified:Direct labour ? ...................3500 hoursDirect material ? ................6000kgMachine hours ? ................2000 hours

Required:(a) Prepare calculations to show, from a financial perspective, the optimum production plan for December and the contribution that would result from adopting your plan.(b) You have now presented your optimum plan to the purchasing and production managers of LM. During the presentation, the following additional information became available:(i) The company has agreed to an order for 250 units of product M For a selling price of $90 per unit from a new overseas customer. This order is in addition to the maximum demand that was previously predicted and must be produced and delivered in December;(ii) The originally predicted resource restrictions were optimistic. The managers now agree that the availability of all resources will be 20 per cent lower than their original predictions.

Construct the revised resource constraints and the objective function to be used to identify, given the additional information above, the revised optimum production plan for December.(c) The resource constraints and objective function requested in part (b)above have now been processed in a simplex linear programming model and the following solution has been printed:

Analyse the meaning of each of the above eight values in the solution to the problem. Your answer should include a proof of the last five of the individual values listed.

Transcribed Image Text:

Product Unit selling price ($) Variable costs per unit: Direct labour ($7 per hour) Direct material ($5 per kg) Machine hours ($10 per hour) 70 90 14 28 10 45 10 20 Fixed overheads absorbed 12 Profit per unit 10 LO Product L other value Product M other value 506 Product L Product M Direct labour Direct material ($) Machine hours Contribution ($) 400 194 312 1.22 312 10934.00