An engineering company has been experiencing problems with restricted availability of resources. The company manufactures a variety of casings. It makes four types of casing. Each casing requires the same bought-in component and some high-grade steel. The standard costs for the four types of casing are as follows:

Casing A B C D

$ $ $ $ Steel 250 500 190 390 Bought-in component 50 50 50 50 Direct labour 60 60 50 100 Variable production costs 40 50 40 50 Fixed production costs 180 240 150 270 Selling and administration costs 145 225 120 215 Profit 35 55 30 55 Selling price 760 1,180 630 1,130 All the selling and administration costs are fixed and the same single component is used for each of the four products. Direct labour is paid $8 per standard hour and each member of the workforce is capable of producing any of the casings. The companys main customer has ordered 30 units of Casing A, 20 units of B, 30 units of C and 20 units of D for production and delivery in the next month. Senior management have agreed that this order should be treated as a priority order and that these casings must be manufactured and delivered to the customer next month. This is necessary to maintain the goodwill of the customer. It is estimated that this order represents 10% of the total demand next month for each type of casing. The company operates a just in time system, and has no inventories of steel, components or finished goods.

Required If the aim is to maximise profit for the month, establish the production and selling plan for the company next month in each of the following situations: 1. Situation 1. Supplies of steel are limited to $250,000. 2. Situation 2. Only 400 bought-in components are available from suppliers. 3. Situation 3. A labour dispute restricts available productive labour hours in the month to 2,125. 4. Situation 4. A labour dispute restricts available productive labour hours in the month to 2,125; But the manufacture of any quantities of the four casings could be sub-contracted to and outside supplier. The cost of buying the casings externally would $475, $705, $380 and $640 for Casing A, Casing B, Casing C and Casing D respectively. In addition, it should be assumed that the major customer insists that its order is completed by the company itself and the manufacture should not be sub-contracted. Each of the restrictions on production should be treated independently, as four different situations.