[F5/Sep 2025] Decision making techniques

Riley Co manufactures two products, the eg and the pey. The following constraints have been identified in relation to labour and machine time:

Labour time 6eg + 4pey ≤ 9,000 hours

Machine time 0.4eg + 0.3pey ≤ 625hours

Maximum demand in the period is 750eg and 1,000pey.

Which of the following is/are slack resources?

• Labour time only

• Machine time only

• Neither labour nor machine time

• Both labour and machine time

Answer explanation

Assuming maximum demand:

Labour time = (6 × 750) + (4 × 1,000) = 8,500 hours, less than the 9,000 hours maximum

Machine time = (0.4 × 750) + (0.3 × 1,000) = 600 hours, less than the 625 hours maximum

Bruno Co manufactures two products, the x and the y. The following constraints apply:

Materials: 4x + 7y ≤ 7,000 kg

Labour time: 8x + 6y ≤ 10,000 hours

x, y > 0

Using simultaneous equations, what is the profit-maximising output of x?

• 500 units

• 875 units

• 1,250 units

• 1,750 units

Answer explanation

Profit-maximising point must be at intersection of 2 constraints (can’t be on x or y axis as x, y > 0 (NOT in this scenario ≥ 0)

8x + 14y = 14,000 Materials equation × 2 Equation 1

8x + 6y = 10,000 Labour equation Equation 2

Subtracting Equation 2 from Equation 1

8y = 4,000, y = 500

Substituting in Equation 2

8x + (6 × 500) = 10,000

8x = 7,000, x = 875

C Co uses material B, which has a current market price of $0.80 per kg. In a linear program, where the objective is to maximise profit, the shadow price of material B is $2 per kg. The following statements have been made:

1. Contribution will be increased by $2 for each additional kg of material B purchased at the current market price

2. The maximum price which should be paid for an additional kg of material B is $2

3. Contribution will be increased by $1.20 for each additional kg of material B purchased at the current market price

4. The maximum price which should be paid for an additional kg of material B is $2.80

Which of the above statements is/are correct?

• 2 only

• 2 and 3

• 1 and 3

• 1 and 4

Answer explanation

(2) is wrong as it reflects the common misconception that the shadow price is the maximum price which should be paid, rather than the maximum extra over the current purchase price. (3) is wrong but could be thought to be correct if (2) was wrongly assumed to be correct.

Which of the following statements about graphical linear programming with the objective of maximising profit is true?

1. If a resource constraint line does not pass through the optimum point on the graph, then the shadow price of that resource is zero

2. The shadow price is the maximum amount a company should pay for one more unit of a scarce resource

3. The slope or gradient of the objective function depends on the amount of resources available to the organisation

• 1 only

• 1 and 2 only

• 2 and 3 only

• 1, 2 and 3

Answer explanation

A resource with a constraint line that does not pass through the optimum point on the graph has a shadow price of zero; another unit of that resource will not change the optimum solution or the contribution earned.

The shadow price is the maximum premium amount that a company should be prepared to pay (i.e. in addition to its existing cost).

The slope or gradient of an objective function to maximise profit depends on the unit contributions of each product.

Which of the following statements about market skimming pricing are true?

1. It is appropriate when the price sensitivity of demand is unknown.

2. It is likely to discourage competitors from entering the market.

3. It is useful when launching a product into a competitive market.

• 1 only

• 2 only

• 3 only

• 1, 2 and 3

Answer explanation

Market skimming uses high prices to maximise the unit profit in the early stages of the product life cycle. This is likely to encourage competitors to enter the market, rather than discourage them. Also, if demand is not known, it will be more beneficial to charge high prices and reduce them if demand is insufficient. It is not appropriate when launching a product into a competitive market as the high price would mean customers would buy from other sources.

The selling price (P) of a product is related to the quantity sold (Q) by the following equation: P = 60 − 0.01Q The total cost is given by TC = 5,000 + 8Q. What selling price will maximise profit?

• $47

• $34

• $26

• $8

Answer explanation

TC = 5,000 (fixed cost) + 8 (variable cost per unit) Q

Marginal cost (MC) = variable cost = 8

Marginal revenue, is given by MR = a − 2bQ where a = 60 and b = 0.01, so MR = 60 − 0.02Q

Profit is maximised at the point where MR = MC

60 − 0.02Q = 8

Therefore, Q = (60 − 8)/0.02 = 2,600 and P = 60 − 0.01(2,600) = $34

Roe sold 2,000 units of a product during the year at a mark-up of 25% on full cost. The selling price was $100 and fixed costs of production were $40,000. Next year the variable costs of production are expected to increase by 10%. Fixed costs of production and sales quantity are expected to remain unchanged. What selling price will maintain the mark-up of 25% on full cost?

• $107.33

• $107.50

• $108.00

• $110.00

Answer explanation

Full costs in current year = (2,000 × $100)/125% = $160,000

Of which, Variable costs = $160,000 − $40,000 = $120,000

Next year:

variable costs = $120,000 × 110% = $132,000

Therefore, total costs = $132,000 + $40,000 = $172,000

To maintain 25% mark-up on cost, sales revenue = $172,000 × 1.25 = $215,000

Therefore selling price per unit = $215,000/2,000 = $107.50

Gemson estimates that at a price of $50 it can sell 2,000 units of its product and at a price of $40 it can sell 2,600 units of the product. What is the price elasticity of demand, to 2 decimal places, when selling price is $50 and quantity sold is 2,000?

• 0.67

• 0.92

• 1.08

• 1.50

Answer explanation

PED = % change in quantity demanded/% change in price

= [(2,600 − 2,000)/2,000 × 100%]/[(40 − 50)/50 × 100%]

= 30%/20% = 1.50

Note: PED ignores the sign (+/-)

A shopkeeper finds that if he sets the price of a particular product at $9.00 per unit he sells, on average, 150 units of the product per month. However, at a price of $10.00 per unit, he sells an average of 110 units per month. What is the price elasticity of demand for the product?

• 0.42

• 2.40

• 0.27

• 0.11

Answer explanation

Proportional change in quantity demanded = 40/150 × 100 = −26.6%

Proportional change in price = 1/9 × 100 = 11.1%

PED = −26.6/11.1 = −2.40

If a 6% fall in price causes a 9% increase in demand for a particular item, what is its price elasticity of demand?

• More than one

• Positive but less than one

• Zero

• Between zero and minus one

Answer explanation

PED = % change in Q/% change in P = 9%/−6% = −1.5

Although PED is almost invariable negative (due to the “inverse” relationship between price and quantity) it is usually stated without the minus sign. Therefore, more than one is the only appropriate answer.