Wanyemba (Pty) Ltd manufactures camping equipment. Management is now considering the introduction of a six-sleeper tent to complement its existing two-sleeper tent. The organisation believes that it can sell all that it produces, but production is limited by labour hours and machine hour manufacturing constraints.

Preliminary analysis has shown the following:

Manufacturing constraints

Wanyemba (Pty) Ltd is limited to 52 500 labour hours in the cutting cost pool and 75 000 machine hours in the make-up cost pool per annum.

Budgeted variable costs per unit and selling price per unit

	2-sleeper (N$)	6-sleeper (N$)
Materials	300	1 150
Labour	100	700
Production overheads	100	150
Selling costs	100	300
Selling price	1 400	3 000

Fixed production overheads

Wanyemba will allocate the fixed production overheads to the two products using an activity-based costing (ABC) system. Total budgeted fixed production overhead cost for each cost pool for the forthcoming year is as follows:

	Overheads per annum (N$)
Quality control	500 000
Cutting	4 000 000
Purchasing	400 000
Make-up	6 000 000

The two products will require the following per single unit of production:

Cost pool	2-sleeper	6-sleeper
Quality control	20 inspections	35 inspections
Cutting	120 labour minutes	360 labour minutes
Purchasing	5 orders	6 orders
Make-up	4 machine hours	8 machine hours

Fixed administration and selling expenses

The total anticipated cost for Wanyemba (Pty) Ltd is N$10 000 000 per annum.

Required:

Calculate the shadow price if any, for machine hours. Assume that the contribution for 2-sleepers is N$1 200 and 6-sleeper is N$2 700. Solve the optimal plan using the algebraic method of linear programming.