Advanced: Optimal output, shadow prices and decision making using the graphical approach Riverside Processors pic recycles by-products
Question:
Advanced: Optimal output, shadow prices and decision·
making using the graphical approach Riverside Processors pic recycles by-products from nearby industrial sites. It produces two products, Ackney and Boylle. The current level of production is 1 00 tonnes of each product per week, but there remains some unused production capacity.
Due to restrictions on the availability of an essential ingredient, Zalium, the maximum weekly output of Ackney is 150 tonnes.
Furthermore, the effluent from the production of Ackney is acid, but is neutralized by effluent from the production of Boylle; as a matter of policy, Riverside restricts the production of Ackney to not more than twice the production of Boylle.
The production process of each of the products requires heat, fuelled by gas. However, Riverside is restricted in the quantity of gas it can use, the maximum being 30 000 therms per week. The production of one tonne of either product requires 100 therms of gas. The production process of both Ackney and Boylle incorporates filtration, and the capacity of the filtration plant is limited to 1750 labour hours per week in normal operation. The production of one tonne of Ackney requires 7 labour hours of filtration, and of one tonne of Boylle, 5 labour hours.
The company is test marketing a new product, Spotz; this requires neither additional process heat nor filtration, although it incorporates the scarce material, Zalium, which is also used in the production of Ackney. The following cost and revenue data are available concerning the three products (in£ per tonne):
The company's fixed fixed costs are £10000 per week.
You are required:
(a) assuming that the new product. Spotz, is not produced, to:
(i) show the feasible outputs of Ackney and Boylle, and to calculate the optimal production plan for Riverside Processors pic, (9 marks)
(ii) calculate the shadow prices of Zalium, filtration plant labour, and process heat for the optimal production plan which you have calculated in (i) above, (5 marks)
(iii) calculate the maximum extra quantity of Zalium (in addition to the 150 units which are available at £27 per unit) which the company should be willing to buy if it could be imported at a price of £50 per unit and if filtration plant throughput cannot be increased;
(6 marks)
(b) assuming that the test marketing campaign for Spotz is successful in demonstrating a sufficient demand at the proposed selling price, and also assuming that no imported Zalium is obtainable, to:
{i) calculate the shadow pnce of Zalium, (2 marks)
{ii) calculate the optimum contribution which Riverside Processors pic can then earn.
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