WZ is a manufacturing company with two factories. The company’s West factory currently produces a number of products. Four of these products use differing quantities of the same resources. Details of these four products and their resource requirements are as follows:

Notes 

1 An analyses of the variable overhead shows that some of it is caused by the number of labour hours and the remainder is caused by the number of machine hours.
2 Currently WZ purchases a component P from an external supplier for \($35\) per component. A single unit of this component is used in producing N the company’s only other product. Product N is produced in WZ’s other factory and does not use any of the resources identified above. Product N currently yields a positive contribution. WZ could manufacture the component in its West factory, but to do so would require: 1 hour of direct labour, 0.5 machine hours, and 2 kgs of direct material B. WZ purchases 500 components per week. WZ could not produce the component in its other factory.
3 The purchasing director has recently advised you that the availability of direct materials A and B is to be restricted to 21 000 litres and 24 000 kgs per week respectively. This restriction is unlikely to change for at least 10 weeks. No restrictions aree expected on any other resources.
4 WZ does not hold inventory of either finished goods or raw materials.
5 WZ has already signed a contract, which must be fulfilled, to deliver the following units of its products each week for the next 10 weeks:

These quantities are in addition to the maxinum demand identified above.
Required:

(a) Calculate whether WZ should continue to purchase the component P or whether it should manufacture it internally during the next 10 weeks.

(b) Prepare a statement to show the optimum weekly usage of the West factory’s available resources.
You are NOT required to use Iinear programming.

(c) (i) Assuming no other changes, calculate the purchase price of the component P at which your advice in part (a) above would change.
(ii) Explain TWO non-financial factors that should be considered before deciding whether or not to manufacture the component internally.

(d) If you were to solve part (b) above using linear programming state the folowing:
•The objective function 

•The inequality for the material A constraint 

•The inequality for the material B constraint

Transcribed Image Text:

J K L M Product $/unit $/unit $/unit $/unit Selling price. 56 40 78 96 Direct labour ($8 per hour) 20 16 Direct material A ($3 per litre) 6 3 Direct material B ($5 per kg) 10 0 201 24 20 15 20 2292 Variable overhead (see note 1) Labour related 1.25 1 1.50 1.25 Machine related 1.25 2 0.75 1 Total variable cost 38.50 22 41.25 51.25 Other data: Machine hours per unit 5 8 3 4 Maximum demand per week 1000 3500 2800 4500