A small car manufacturer builds three types of cars: type 1, 2 and 3. Type 1 sells at a profit of R45, type 2 at a profit of R50, and type 3 at a profit of R55. The management wishes to know how many of each carton type should be made to produce maximum profit. The factory is divided into two sections. Section A does the moulding and construction work, while section B does the painting and finishing depending on customer requirements. Type 1 takes 2 hours in section A and 1.5 hours in section B. Type 2 takes 2.5 hours in A and 2 hours in B. Type 3 takes 3 hours in A and 1 hour in B. Section A has a total of 4006 hours available, and section B has 2495 hours available. The final product has to go through quality assurance. The company has at most 1500 hours allocated for quality assurance checks. It takes 1 hour for type 1, 0.75 for type 2 and 1.25 for type 3 to check the quality of the final product.

1.1 Formulate the problem mathematically. [3]

1.2 Write the problem in canonical form. [3]

1.3 Set up the initial simplex tableau and indicate the pivot element. (Do not solve the problem). [3]