PM- Limiting Factor

An organisation has the following contribution function:

Contribution = 5X + 1OY

where

X = the number of units of product X produced, and

Y = the number of units of product Y produced.

A graph has identified that the optimal production plan exists at the point where the

following two constraints cross:

Skilled labour: 6X + 4Y <= 62,000

Unskilled labour: 2X + 5Y <= 50,000

There is a maximum demand of 12,000 units of each product.

What is the number of units of Product Y produced in order to maximise contribution (to

the nearest whole unit)?

• 8000

• 9000

• 7000

• 6000

A jewellery company makes rings (R) and necklaces (N).

The resources available to the company have been analysed and two constraints have been

identified:

Labour time 3R + 2N <= 2,400 hours

Machine time O.5R + O.4N <= 410 hours

The management accountant has used linear programming to determine that R = 500 and

N = 400.

Which of the following is/are slack resources?

(1) Labour time available

(2) Machine time available

• (1) only

• (2) only

• Both (l) and (2)

• Neither (I) nor (2)

Q plc makes two products — Quone and Qutwo — from the same raw material. The selling

price and cost details of these products are as shown below:

The maximum demand for these products is 500 units per week for Quone, and an

unlimited number of units per week for Qutwo.

What is the shadow price of these materials, if material were limited to 2,000 kgs per

week?

• $nil

• $2.00 per kg

• $2.66 per kg

• $3.40 per kg

The shadow price of skilled labour for CBV is currently $8 per hour. What does this mean?

• The cost of obtaining additional skilled labour resources is $8 per hour

• There is a hidden cost of $8 for each hour of skilled labour actively worked

• Contribution will be increased by $8 per hour for each extra hour of skilled labour

  that can be obtained

• Total costs will be reduced by $8 for each additional hour of skilled labour that can be

  obtained

The following details relate to three services provided by RST Company:

All three services use the same type of direct labour which is paid $25 per hour.

The fixed overheads are general fixed overheads that have been absorbed on the basis of

machine hours.

What are the most and least profitable uses of direct labour, a scarce resource?

• Most profitable - S

  Least profitable - R

• Most profitable - S

  Least profitable - T

• Most profitable - T

  Least profitable - R

• Most profitable - T

  Least profitable - S

A linear programming model has been formulated for two products, X and Y. The objective

function is depicted by the formula C = 5X + 6Y, where C = contribution, X = the number of

product X to be produced and Y = the number of product Y to be produced.

Each unit of X uses 2 kg of material Z and each unit of Y uses 3 kg of material Z. The

standard cost of material Z is $2 per kg.

The shadow price for material Z has been worked out and found to be $2.80 per kg.

If an extra 20 kg of material Z becomes available at $2 per kg, what will the maximum

increase in contribution be?

• Increase of $96

• Increase of $56

• Increase of $16

• No change

An organisation is experiencing a shortage of resources and has graphed a potential linear

programming solution which shows its first product, televisions, on the horizontal axis and

its other product, tablet computers, on the vertical axis.

The iso-contribution line to solve the linear programme is very flat and downward sloping.

Which of the following statements is likely to be true for the company?

• The contribution per unit for tablet computers must be higher than that for

  televisions

• The contribution per unit for televisions must be higher than that for tablet

  computers

• The contribution per unit for each type of product is very similar

• The contribution per unit for one of the products must be negative

An organisation has the following contribution function:

Contribution = 12A + 8B, where

A = the number of units of product A produced, and

B = the number of units of product B produced.

A graph has identified that the optimal production plan exists at the point where the

following two constraints cross:

Material X: A + 2B <= 8,000

Material Y: 2A + B <= 13,000

There is a maximum demand of 10,000 units of each product.

How many units of Product A are produced in order to maximise contribution?

• 0

• 1,000

• 6,000

• 10,000

An organisation has graphed the following linear programming model:

All constraints have less than or equal to constraints.

What is the maximum number of units of Product B which can be produced?

• 20

• 40

• 60

• 80