Scope Ltd manufactures two types of engines - Diesel engine and Petrol engine. Both products go through the Assembly Department and Quality Control Department. The available machine hours for both the Assembly and Quality Control departments is limited. The Assembly Department has 600 machine hours per day and the Quality Control Department has 120 machine hours per day. Additional capacity cannot be obtained in the short run. The company can sell as many engines as it produces. The following data is provided:

Diesel engine

(per unit)

Petrol engine

(per unit)

Selling price

$1000

$600

Direct material

$250

$180

Direct labour

$300

$200

Variable manufacturing overhead

$150

$100

Hours required per engine in Assembly Department

5 hours

2 hours

Hours required per engine in Quality ControlDepartment

0.5 hours

1 hour

Required:

(a)Formulate the objective function to maximize the contribution margin.(1 mark)

(b)Formulate the constraints based on the limited machine hours available.(2 marks)

(c)Graph the constraints and determine how many units of each type of engine should be produced at the optimal point.(5 marks)