IM26.1 Intermediate: Optimal output using the graphical approach. IM26.4 Advanced Optimal output and shadow prices using the graphical approach Urine Lid is a company whose objective is to maximize profits. It manufactures two specis ty chemica G Limited, manufacturers of superior garden omaments, is preparing its production budget for powders, gamma and delta, using three processes: heating, refining and blending. The powders the coming period. The company makes four types of omament, the data for which are as can be produced and sold in indefinitely divisible quantities. follows: The following are the estimated production hours for each process per kilo of output for each of Product Pixie Elf Queen King the two chemical powders during the period 1 June to 31 August: (E per unit) (E per unit) (E per unit) (E per unit) Direct materials 25 35 22 25 Gemma (hours) Delta (hours) Variable overhead 17 18 15 16 Heating 400 120 Selling price 111 98 122 326 Refining 100 90 Blending 100 250 Direct labour Hours Hours Hours Hours hours: per unit per unit per unit per unit During the same period, revenues and costs per kilo of output are budgeted as Type 1 Type 2 10 Gemma Delta Type 3 25 [E per kilo) (E per kilo) Selling price 18.000 25.000 Fixed overhead amounts to $15,000 per period. Variable costs 12.000 17.000 Contribution 4.000 8.000 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. It is anticipated that the company will be able to sell all it can produce at the above prices, and that at any level of output fixed costs for the three month period will total $38,000 The maximum hours available in each type are: Type 1 8.000 hours The company's management accountant is under the impression that there will only be one Type 2 20.000 hours scare factor during the budget period, namely blending hours, which cannot exceed a total of Type 3 25.000 hours 1050 hours during the period 1 June to 31 August. He therefore correctly draws up an optimum production plan on this basis. The marketing department judges that, at the present selling prices, the demand for the products is likely to be: However, when the factory manager sees the figures he points out that over the three month Pixie Unlimited demand period there will not only be a restriction on blending hours, but in addition the heating and Elf Unlimited demand refining hours cannot exceed 1,200 and 450 respectively during the three month period. Queen 1.500 units King 1,000 units Requirements: Calculate the initial production plan for the period 1 June to 31 August as prepared You are required: by the management accountant, assuming blending hours are the only scare factor. to calculate the product mix that will maximize profit, and the amount of the profit Indicate the budgeted profit or loss and explain why the solution is the optimum b) to determine whether it would be worthwhile paying for Type 1 Labour for overtime b) Calculate the optimum production plan for the period 1 June to 31 August, allowing working at time and a half and, if so, to calculate the extra profit for each 1,000 hours for both the constraint on blending hours and the additional restrictions identified by of overtime; the factory manager, and indicate the budgeted profit or loss. c) to comment on the principles used to find the optimum product mix in part (a). State the implications of your answer in (b) in terms of the decisions that wil have to pointing out any possible limitations; be made by Using Lid with respect to production during the period 1 June to 31 d) to explain how a computer could assist in providing a solution to the data shown August after taking into account all relevant costs. above. Under the restrictions identified by the management accountant and the factory manager, the shadow (or dus ) price of one extra hour of blending time on the optima production plan is $27.50. Calculate the shadow (or dual) price of one extra hour of refining time. Explain how such information might be used by management, and in so doing indicate the limitations inherent in the figures. Note: ignore taxation