Woodalt plc has two automated machine groups X and Y, through which timber is passed in order to produce two models of an item of sports equipment. The models are called ?Traditional? and ?Hightech?.The following forecast information is available for the year to 31 December:

(iii) Machine groups X and Y have maximum operating hours of 3400 and 3840, respectively. The sports equipment production is the sole use available for the production capacity.(iv) The maximum quantity of timber available is 34 000 metres.Each product unit requires four metres of timber. Timber may be purchased in lengths as required at ?5 per metre.(v) Variable machine overhead cost for machine groups X and Y is estimated at ?25 and ?30 per machine hour, respectively.(vi) All units are sold in the year in which they are produced.

A linear programme of the situation has been prepared in order to determine the strategy which will maximize the contribution for the year to 31 December and to provide additional decision-making information. Appendix 3.1 below shows a print-out of the solution to the LP model.

Required:(a) Formulate the mathematical model from which the input to the LP programme would be obtained. ?(4 marks)(b) Using the linear programme solution in Appendix 3.1 where appropriate, answer the following in respect of the year to 31 December:(i) State the maximum contribution and its distribution between the two models.(ii) Explain the effect on contribution of the limits placed on the availability of timber and machine time.(iii) In addition to the sports equipment models, Woodalt plc has identified additional products that could earn contribution at the rate of ?20 and ?30 per machine hour for machine groups Xand Y, respectively.Such additional products would be taken up only to utilize any surplus hours not required for the sports equipment production.Prepare figures that show the additional contribution which could be obtained in the year to 31 December from the additional sales outlets for each of machine groups X and Y.(iv) Explain the sensitivity of the plan to changes in contribution per unit for each sports equipment product type.

(v) Woodalt plc expects to be able to overcome the timber availability constraint. All other parameters in the model remain unchanged. (The additional products suggested in (iii) above do not apply.)Calculate the increase in contribution which this would provide.(vi) You are told that the amended contribution maximizing solution arising from (v) will result in the production and sale of the ?Traditional? product being 3600 units.Determine how many units of the ?Hightech? product will be produced and sold.?

(c) Suggest ways in that Woodalt plc may overcome the capacity constraints that limit the opportunities available to it in the year to 31 December. Indicate the types of cost that may be incurred in overcoming each constraint.(d) Explain why Woodalt plc should consider each of the following items before implementing the profit maximizing strategy indicated in Appendix 3.1:(i) Product specific costs;(ii) Customer specific costs;(iii) Life cycle costs.Your answer should include relevant examples for each of (i) to (iii).

Appendix 3.1Forecast strategy evaluation for the year to 31 December Target cell (max) (?)

Adjustable cells (units)

Adjustable cells (units and ?)

Constraints (quantities and ?)

Transcribed Image Text:

"Traditional' 'Hightech' (i) Maximum sales potential (units) (ii) Equipment unit data: Selling price Machine time: group X (hours) 6000 10000 £100 0.5 £90 0.3 0.45 group Y (hours) 0.4 Cell Name Final value $C$2 Contribution 444 125