Over the years, BMW has earned an enviable reputation for quality-built cars.

To ensure they maintain their reputation, BMW is considering the possibility of acquiring 3 computer-controlled machines that will hopefully increase contribution margins. The new computer-controlled machines will have in total an annual capacity of 13,525 hours. Each Super Luxury unit will require 150 hours of computer-controlled machine hours, while each unit of the Luxury models will require 125 hours and each unit of the Affordable Luxury models 100 hours.

With no change in the selling price, the new average contribution margin for BMWs 3 luxury models will be, respectively, $17,000, $14,000, and $9,500 for the Super Luxury, Luxury, and Affordable Luxury.

The product mix is constrained by the demand for each type of car. The maximum demand for each type is estimated at 30 units for the Super Luxury, 45 units for the Luxury, and 65 units of the Affordable Luxury.

The maximum number of vehicles that can be produced equals 110.

To solve this problem, the plant manager has set up the following linear program:

Maximize: C (S, L, A) =?

Subject to: ?

Where: S represents the number of Super Luxury units sold

L represents the number of Luxury units sold

A represents the number of Affordable Luxury units sold

REQUIRED:

a. Determine the maximization formula. formula out in your Excel solution. (1 mark)

b. Determine the constraints. Write these constraints out in your Excel solution. (3 marks)

Use solver to answer the following questions:

c. Calculate the total contribution margin. (2 marks)

d. What would the net increase in contribution margin be if demand for Luxury models increased from 45 to 53? (2 marks)

e. Identify two other factors that BMW should consider before making a decision on whether to buy the machines. (Make sure each of your answers is fully explained.) (2 marks)