Question 1

A company accountant is trying to determine the optimum production plan for the period using linear programming.
The accountant has correctly formulated the linear programming problem as follows:
Variables (products): x and y
Objective function: Maximise contribution, C = 10x + 15y
Material constraint: 4x + 6y 500 (kg)
Labour constraint: x + 2y 350 (hours)
Machine constraint: 10x + 4y 1,500 (hours)
x constraint: 50 x 200
y constraint: y 0
Which of the following statements is true?

Options :

A : The selling price of y is $15.

B : The maximum demand for product x is 50 units.

C : Product x requires twice as much labour time as Product y.

D : Product y requires 4 machine hours to manufacture.

Answer: D

Question 2

Some of the movements in a time series follow a pattern over time.
Which type of movement does NOT follow a pattern over time?

Options :

A : Trend

B : Cyclical variation

C : Random variation

D : Seasonal variation

Answer: C

Question 3

THS produces two products from different combinations of the same resources. Details of the products are shown below:

Identify, using graphical linear programming, the optimal production plan for products E and R to maximize THS's profit in the month.

Options :

A : The solution (from the graph0 is to produce 675 units of E and 470 units of R.

B : The solution (from the graph0 is to produce 495 units of E and 670 units of R.

C : The solution (from the graph0 is to produce 475 units of E and 770 units of R.

D : The solution (from the graph0 is to produce 375 units of E and 750 units of R.

E : The solution (from the graph0 is to produce 375 units of E and 870 units of R.

F : The solution (from the graph0 is to produce 495 units of E and 470 units of R.

Answer: D

Question 4

A university is trying to decide whether or not to advertise a new post-graduate degree programme. The number of students starting the programme is dependent on economic conditions. If conditions are poor, it is expected that the programme will attract 40 students without advertising. There is a 60% chance that economic conditions will be poor. If economic conditions are good it is expected that the programme will attract only 20 students without advertising. There is a 40% chance that economic conditions will be good.

If the programme is advertised and economic conditions are poor, there is a 65% chance that the advertising will stimulate further demand and student numbers will increase to 50. If economic conditions are good, there is a 25% chance the advertising will stimulate further demand and numbers will increase to 25 students.

The profit expected, before deducting the cost of advertising, at different levels of student numbers are as follows:

The cost of advertising the programme will be $15,000.

Required:

Demonstrate, using a decision tree, whether the programme should be advertised.

Options :

A : Yes, the programme should be advertised as the profit will be $82000

B : Yes, the programme should be advertised as the profit will be $92000

C : No, the programme should not be advertised as there will be a loss $82000

D : No, the programme should not be advertised as there will be a loss $92000

Answer: A

Question 5

Two products being produced by a company require the same material which is limited to 2,600 kgs.

What is the optimal production plan?

Options :

A : 500 units of S & 100 units of T

B : 50 units of S & 400 units of T

C : 400 units of S & 167 units of T

D : 500 units of S & 400 units of T

Answer: A