The managing director of H Limited is setting the production plan for the next financial year. H has a shortage of skilled labour and wishes to maximise the profitability of the company. H manufactures three products X, Y and Z. There is 200 000 hours of skilled labour available in the year at a cost of $10 per hour. The following information relates to each product.
Assuming all relevant information is provided, in what order should H manufacture its products to maximise profit in the current year?

Question

The managing director of H Limited is setting the production plan for the next financial year. H has a shortage of skilled labour and wishes to maximise the profitability of the company. H manufactures three products X, Y and Z. There is 200 000 hours of skilled labour available in the year at a cost of $10 per hour. The following information relates to each product. 
Assuming all relevant information is provided, in what order should H manufacture its products to maximise profit in the current year?

Quizplus · Accepted Answer

To maximise profit, H should prioritise producing the products with the highest contribution per hour of skilled labour.

Product X: contribution per hour = $30 - $10 = $20
Product Y: contribution per hour = $20 - $10 = $10
Product Z: contribution per hour = $25 - $10 = $15

Therefore, H should manufacture product X first (using 50,000 hours of skilled labour) to generate a contribution of $1,000,000. Then they should manufacture product Z (using 100,000 hours of skilled labour) to generate a contribution of $1,500,000. Finally, they can manufacture product Y (using 50,000 hours of skilled labour) to generate a contribution of $500,000.

This gives a total contribution of $3,000,000, which is the maximum possible given the constraints.

The Managing Director of H Limited Is Setting the Production