QUESTION $3$

Activon Group $($AG$)$ is involved in the business of venue management for sporting activities. The

company actively seeks out suitable premises to be rented and converted into venues for

sporting activities such as futsal, badminton, tennis, ice$-$skating and basketball. Customers are

charged a fee for the use of the sporting facilities.

The company has recently identified three suitable premises that could potentially be rented and

converted into a venue for futsal. However, the company intends to rent only one of the three

premises as they are in proximity to each other. The three premises vary in size and shape. As

such, the number of futsal pitches that can be accommodated in each of the three premises will

differ. The information relating to the three premises is as follows:

Annual rental cost Maximum fee$-$generating

hours per annum

Premises A $110,00021,000$

Premises T $260,00042,400$

Premises V $410,00074,100$

Regardless of the choice of premises, the company will be subject to uncertainty in relation to the

level of demand for the year. The possible levels of demand are as follows:

Number of hours per annum $,$ Probability

High demand $-68000,35\%$

Medium demand $-45000,45\%$

Low demand $-19000,20\%$

The company intends to charge a fee of $12$ per hour for the use of the futsal pitches. Regardless of the level of demand, the company will only be able to earn fee income up to the maximum fee$-$generating hours. The company will not be able to earn any income on spare capacity in excess of demand. Other than the rental cost, the company will also have to incur an annual fixed cost amounting to $60,000.$ The contribution rate is $75\%.$

Required:

a$)$ Prepare a summary that tabulates the annual profit for each of the nine possible outcomes.

$(6$ marks$)$

b$)$ Determine the choice of premises using the following decision rules:

$($i$)$ Maximin

$($ii$)$ Maximax

$($iii$)$ Regret criterion

$($iv$)$ Expected value

$(13$ marks$)$

c$)$ Compute the maximum price that AG should be willing to pay for information that could

perfectly indicate the level of demand.

$(4$ marks$)$

d$)$ Assume that a consultant will only be able to predict the level of demand with an $80\%$ level of accuracy. This means that the consultant will provide an inaccurate prediction $20\%$ of the

time and the inaccurate predictions are equally distributed between the other two states of nature.

Formulate the number of days matrix to incorporate the imperfect information into the probabilities of the states of nature.

$(7$ marks$)$

$($Q$3$ Total $30$ marks$)$