PQR Limited is an engineering company engaged in the manufacture of components and finished products. The company

Question:

PQR Limited is an engineering company engaged in the manufacture of components and finished products.
The company is highly mechanized 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. Overhead absorption rates per machine hour are as follows:

2 Components A and B are NOT used in finished products C and D. They are used in the company's other products, none of which use the drilling or grinding machines. The company does not manufacture any other components.
3 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.
4 The maximum demand in units per week for each of the finished products has been estimated by the marketing director as:
Product ....................................C 250 units
Product ....................................D 500 units
5 The internal demand for components A and B each week is as follows:
Component A................................ 50 units
Component B.............................. 100 units
6 There is no external market for components A and B.
7 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 maximize its profits, and the profit per week that this should yield.
(b) (i) The production director has now discovered that he can obtain unlimited quantities of components identical to A and B for £50 and £96 per unit respectively. State whether this information changes the production plan of the company if it wishes to continue to maximize
its profits per week. If appropriate, state the revised production plan and the net benefit per week
caused by the change to the production plan.