Ltd started off producing a single product, called A. Price and cost details per unit are:

		R
Selling Price		R275
Direct Material	5kgs at R20/kg	R100
Direct Labour	4 hours at R25/hr	R100
Manufacturing Overhead		R70
Net Profit		R5

Product A, requires 10 hours of machine time. Actual manufacturing overheads are incurred according to the following cost volume relationship:

Overheads	R325 000	R700 000
Machine Hours	25 000	100 000

After the initial startup of selling a single product A [Note this information is as per Test 2], Ltd, added Product B. The income statement for the most recent financial year is:

	Product A	Product B	Total
Sales Units	5 000	5 000	10 000
Price	R275	R525
	R000s	R000s	R000s
Sales Value (R000s)	1 375	2 625	4 000
Cost of Sales (R000s)			3 700
Raw Material	500	1 100	1 600
Direct Labour	500	375	875
Manufacturing Overhead - Variable - Fixed	250	625	875 350
Normal Gross Profit (R000s)			300
Under-recovered overhead			50
Variable selling (Product B only)			100
Actual net profit (R000s)			150

Notes to the income statement:

a. Each unit of product A requires R100 of raw material, 10 hours of machine time and 4 hours of labour time.

b. Each unit of product B requires R220 of raw material, 25 hours of machine time and 3 hours of labour time.

c. Labour time is restricted to 60 000 hours, and cannot be increased.

d. Maximum machine time capacity is 200 000 hours. Due to Covid-19, the plant was operating at a level that represents 87.5% of maximum capacity. The fixed costs have been recovered on machine hours. The pre-determined recovery rate was based on machine time equal to 100% of capacity and a budgeted fixed manufacturing cost of R400 000. Variable manufacturing overhead is incurred on a machine hour basis.

e. Actual fixed manufacturing overheads had doubled from the initial start-up situation (R200 000), when only product A was produced.

f. Selling expenses are incurred for product B only.

QUESTIONS:

1. Define the variables

2. Establish the objective function

3.Establish the limiting factors

4. Determine and rank the contribution per limiting factor

5. Draw a graph of the constraints for which linear programming is required

6. Establish the feasible region

7. Determine the optimal product mix