QUESTION $1$

$($a$)$ A certain product under development took $200$ hours for the production of its $2$ nd unit

and $180$ hours for its $4$ th unit.

$($i$)$ What is the learning rate? $(4$ marks$)$

$($ii$)$ How much time did the first unit take? $(6$ marks$)$

$($b$)$ A firm is about to undertake the manufacture of a product, and is weighing three capacity

alternatives: small job shop, large job shop, and repetitive manufacturing. The small job

shop has fixed costs of $3,000$ per month, and variable costs of $10$ per unit and a

capacity of $1000$ units per month. The larger job shop has fixed costs of $12,000$ per

month and variable costs of $3$ per unit and a monthly capacity of $4,000$ units. The

repetitive manufacturing plant has fixed costs of $30,000$ and variable costs of $1$ per unit

and a monthly capacity of $2,500$ units.

Demand for the product is expected to be $500$ units with "poor" market acceptance,

$1,500$ units per month with "moderate" market acceptance, but $4,000$ under "strong"

market acceptance. The probability of poor market acceptance is $20\%,$ moderate

acceptance is estimated to be $50\%$ strong acceptance has a probability of $30\%.$ The

product will sell for $50$ per unit regardless of the capacity decision. Which capacity

choice should the firm make?

$($a$)$ What is the profit associated with each of the nine outcomes? $(10$ marks$)$

$($b$)$ Draw a decision tree for the company. $(5$ marks$)$

$($c$)$ Using the information from the decision tree, calculate the expected profit of each

capacity alternative. Which option will the firm's management prefer if he wants to

maximise his expected profit? $(5$ marks$)$