Linear Programming 10 Marks Question 3 Study the scenario and complete the question that follows: Duntop (Pty) Limited manufactures tyres for cars and bakkies. Speedy tyres are manufactured for cars and Bumpy tyres for bakkies. Mr Mugabe, the managing director has provided you with the following information. The results of a market survey show that 50 000 Speedy and 40 000 Bumpy tyres can be sold at prices of R200 and R240 per tyre respectively. A shortage of material exists, resulting in only R 4 620 000 being available annually. The flexible budget, at capacity levels of 90% and 100%, indicates that total overheads will amount to R7 984 000 and R8 200 000 for 24 300 and 27 000 machine hours respectively. The prime cost per tyre is as follows: Speedy Bumpy R R Material 55 Direct labour @ R50 per hour 35 80 90 The machining of a Speedy tyre takes 15 minutes and that of a Bumpy tyre 22.5 minutes. Source: Hunde, T. (2020) 50 30 Required: Determine the product mix which will maximize the income of the company, assuming a capacity utilization of 100% in terms of machine hours. (10 Marks) Linear Programming 10 Marks Question 3 Study the scenario and complete the question that follows: Duntop (Pty) Limited manufactures tyres for cars and bakkies. Speedy tyres are manufactured for cars and Bumpy tyres for bakkies. Mr Mugabe, the managing director has provided you with the following information. The results of a market survey show that 50 000 Speedy and 40 000 Bumpy tyres can be sold at prices of R200 and R240 per tyre respectively. A shortage of material exists, resulting in only R 4 620 000 being available annually. The flexible budget, at capacity levels of 90% and 100%, indicates that total overheads will amount to R7 984 000 and R8 200 000 for 24 300 and 27 000 machine hours respectively. The prime cost per tyre is as follows: Speedy Bumpy R R Material 55 Direct labour @ R50 per hour 35 80 90 The machining of a Speedy tyre takes 15 minutes and that of a Bumpy tyre 22.5 minutes. Source: Hunde, T. (2020) 50 30 Required: Determine the product mix which will maximize the income of the company, assuming a capacity utilization of 100% in terms of machine hours. (10 Marks)