G Limited, manufacturers of superior garden ornaments, is preparing its production budget for the coming period. The company makes four types of ornament, the data for which are as follows: Product Direct materials Variable overhead Selling price Pixie ( per unit) 25 17 111 Elf ( per unit) 35 18 98 Queen ( per unit) 22 15 122 King ( per unit) 25 16 326 Direct labour Hours Hours Hours Hours hours per unit per unit per unit per unit Type 1 8 6 Type 2 10 10 Type 3 5 25 Fixed overhead amounts to 15,000 per period. Each type of labour is paid 5 per hour but because of the skills involved, an employee of one type cannot be used for work normally done by another type. The maximum hours available in each type are Type 1 8,000 hours Type 2 20,000 hours Type 3 25,000 hours The marketing department judges that at the present selling prices, the demand for the products is likely to be Pixie Unlimited demand Elf Unlimited demand Queen 1,500 units King 1,000 units You are required: a) to calculate the product mix that will maximize profit, and the amount of the profit, b) to determine whether it would be worthwhile paying for Type 1 Labour for overtime working at time and a half and, if so, to calculate the extra profit for each 1,000 hours of overtime c) to comment on the principles used to find the optimum product mix in part (a) pointing out any possible limitations, d) to explain how a computer could assist in providing a solution to the data shown above