QUESTION 1 : [17 MARKS]

Willy Wonkas Chocolate Company manufactures two products, Skittles and Peanut Clusters. The firm has two main resources: its machine operators (labour force) and a supply of cocoa for use in the chocolate making process. During the next production cycle, 1200 hours of labour are available under a union agreement. The firm also has a stock of 3500kg of good quality cocoa. Each batch of Skittles that Willy Wonka produces requires 4 labour hours and 10kg of cocoa; each batch of Peanut Clusters produced takes 6 labour hours and 35kg of cocoa. Completed Skittles will yield a profit of R9,00 per batch, and Peanut Clusters will result in a profit of R20 per batch. How many batches of Skittles and Peanut Clusters should Willy Wonka produce to obtain the largest possible profit? Use the graphical corner point method approach in order to solve the problem.

If S = Skittles and P = Peanut Clusters

Then,

1.1. Maximum Profit = ?

1.2. The constraint equation for Skittles is ?

1.3. The constraint equation for Peanut Clusters is .?

1.4. The value for S is always .............?

1.5. The value for P is always ...........?

1.6. Using the constraint equation for Skittles, calculate the value for P .

1.7. Using the constraint equation for Skittles, calculate the value for S ..

1.8. Using the constraint equation for Peanut Clusters, calculate the value for P .

1.9. Using the constraint equation for Peanut Clusters, calculate the value for S .

1.10. Using the graphical corner point method, the maximum profit to be made is R

1.11. At the maximum profit, the amount of Skittles to be manufactured is batches.

1.12. At the maximum profit, the amount of Peanut Clusters to be manufactured is batches.