Smith’s Ltd is a family-run business that manufactures specialized building plastics. It began trading in 2010. The company is facing constraints on both labour and materials due to a current shortage in supply of skilled labour and political unrest in the country of an oversea supplier. It cannot produce enough skirting boards and drainage pipes to satisfy market demand.

The maximum labour hours available are 17,280 and the maximum materials available are 20,640 kg. Each skirting board takes 18 hours to make and uses 24 kg of material. Each drainage pipe takes 24 hours to make and uses 12 kg of material. Labour is paid at a rate of £30 per hour and materials cost £22.5 per kg. The selling price for skirting board is £1,550 and the selling price for drainage pipe is £1,650. Variable overheads are charged at £15 per labour hour. Fixed costs are £50,000 per annum.

Required:

• a. Calculate the contribution per skirting board and drainage pipe. Using linear programming simultaneous equations, calculate the optimum product mix for Smith’s Ltd together with the contribution and the profit that this generates for the company.