Intermediate: Allocation of scarce capacity and make or buy decision where scarce capacity exists PQR Limited is an engineering company engaged in the manufacture of components and finished products. The company is highly mechanised and each of the components and finished products requires the use of one or more types of machine in its machining department. The following costs and revenues (where appropriate) relate to a single component or unit of the finished product:

1. The labour hour rate is £5 per hour.
2. Overhead absorption rates per machine hour are as follows:

3. Components A and B are NOT used in finished products C and D. They are used in the com¬ pany’s other products, none of which use the drilling or grinding machines. The company does not manufacture any other components.
4. The number of machine drilling hours available is limited to 1650 per week. There are 2500 machine grinding hours available per week. These numbers of hours have been used to calculate the absorption rates stated above.
5. The maximum demand in units per week for each of the finished products has been estimated by the marketing director as:

6.The internal demand for components A and B each week is as follows:

7. There is no external market for components A and B.
8. PQR Limited has a contract to supply 50 units of each of its finished products to a major customer each week. These quantities are included in the maximum units of demand given in note 5 above.
Requirement:

(a) Calculate the number of units of each finished product that PQR Limited should produce in order to maximise its profits, and the profit per week that this should yield. (12 marks)

(b) (i) The production director has now discov¬
ered that he can obtain unlimited quan¬ tities of components identical to A and B for £50 and £96 per unit respectively.
State whether this information changes the production plan of the com¬ pany if it wishes to continue to maximise its profits perweek. Ifappropriate, state the revised production plan and the net benefit per week caused by the change to the production plan. (7 marks)
(ii) The solution of problems involving more than one limiting factor requires the use of linear programming.
Explain why this technique must be used in such circumstances, and the steps used to solve such a problem when using the graphical linear program¬ ming technique.

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Components Finished products A& B C D Selling price Direct materials 127 161 Direct wages 10 80 29 33 38 30 20 25 Variable overhead: Drilling 6 3 9 12 Grinding 8 16 4 12 Fixed overhead: Drilling Grinding Total cost PAM 12 6 18 10 20 54 104 89 858 24 15 126