QUESTION 4

Sunlux Consulting cc specialises in two types of consultancy project. Each type A project requires twenty hours of work from qualified researchers and eight hours of work from junior researchers Each type B project requires twelve hours of work from qualified researchers and fifteen hours of work from junior researchers Researchers are paid on an hourly basis at the following rates:

Qualified researchers	N$30 / Hour
Junior researchers	N$14 / Hour

Other data relating to the project are:

Details	A	B
	N$	N$
Revenue per project	1,700	1,500
Direct project expenses	408	310
Administration	280	270

**Administration costs are attributed to projects using a rate per project hour. Total administration costs are N$28 000 per four week period. During the four week period ending on 30 June 2022, owing to holidays and other staffing difficulties the number of working hours available are:

Qualified researchers	1,344
Junior researchers	1120

An agreement has already been made for twenty type A projects with Windhoek Limited. Sunlux Consulting must start and complete these projects in the four week period ending 30 June 2022. A maximum of 60 type B projects may be undertaken during the four week period ending 30 June 2022. Sunlux Consulting is preparing its detailed budget for the four week period ending 30 June 2022 and needs to identify the most profitable use of the resources it has available.

REQUIRED:

4.1) Formulate the linear programming model for the four week period ending 30 June 2022 in standard format.

4.2) Calculate using the graphical method, the mix of projects that will maximise profit for Sunlux Consulting for the four week period ending 30 June 2022.

4.3) Explain the importance of identifying scarce resources when preparing budgets and the use of linear programming to determine the optimum use of resources.