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Q.3. The Hot-Bake shop sells only bread made that day. Each loaf

produced has a variable cost of 30p and sells for SOp. Any bread

unsold at the end of each day is thrown away.

At the start of each day, the manager must decide how many loaves

to produce. The table below records sales over the past month:

Daily sales Frequency

1000 6

1200 10

1400 10

1600 4

(a) Fixed costs are estimated at X per day. Find the breakeven

number of loaves produced and sold, and the number if expected

daily profit was 50.

(b) Find the number of loaves produced to minimise expected

opportunity loss.

(c) Bread is produced by a fully automated machine which mixes the

dough, divides it into 1 lb units, fills each baking tin and passes

them through an oven. Out of each batch, some are rejected for

being underweight or burnt.

The proportion rejected has the probability distribution given

below:

Proportion rejected

0.05

0.10

0.15

Probability

0.25

0.60

0.15

(i) Find the number of loaves produced if the expected number of saleable loaves equals your answer to question (b).

(ii) The services of a maintenance engineer would set the

rejection rate equal to 0.05, but would cost 11 per day.

Advise the manager on whether to engage the engineer or

not, if the desired daily production is 1300.

(d) Comment on the assumptions underlying your answers, and

discuss the relevance of other decision criteria.

4. 'Profit is the maximum value a company can distribute during the

year and still expect to be worth as much at the end of the year as it

was at the beginning.' Discuss this statement, and comment on its

value in measuring profit for decision-making

3.33 Suppose a certain type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probabil- ity density function that characterizes the proportion Y that make a profit is given by f ( y ) = ky* (1 - y)3, 0