Question 4 (6 points) Daily sales of bread by Salvador\'s Baking Company follow

Question

Question 4 (6 points) Daily sales of bread by Salvador's Baking Company follow the historical pattern shown in the table below. It costs the bakery 40 cents to produce a loaf of bread, which sells for 85 cents. Any bread unsold at the end of the day is sold to the parish jail for 10 cents per loatf Demand 500 600 700 800 900 Probability 20 2040 15 05 a) Construct the decision table of conditional payoffs. (2 points) b) How many loaves should Sal bake each day in order to maximize contribution? (2 points) c) What would the company's manager be willing to pay for a forecast that would accurately determine the level of demand in the future? (2 points) Hint: This question is similar to Q2 in your homework)

Explanation / Answer

a)

selling price of a loaf is 85 cents and cost is 40 cents

If sold, contribution is 45 cents.

If unsold contribution is -30 cents.

Example when the supply is 500 breads and the demand is 600 breads then payoff is

500*45+100*(-30) = 19500

when the supply is 900 breads and the demand is 700 breads then payoff is

700*45+200*(-30) = 25500

when the supply is 600 breads and the demand is 800 then payoff is

600*45+200*0 = 27000

b)

To maximise contribution, he has to be an optimist that gives the maximum payoff.

This happens when he makes 900 breads and the supply is 900 where the payoff is 40500

c)

Find the expected payoff for each of the supply. for example for 600 breads.

expected pay off = 19500*0.2+27000*0.2+27000*0.4+27000*0.15+27000*0.05=25500

if there is excess demand ( supply < demand), then we will miss out on profit of (demand-supply) *45

if there is excess supply (supply > demand) then we will suffer loss of (supply - demand) *30

Multiply with the probabilities and sum on each of the columns.

Average is 5250, so he can pay that much for an accurate forecast.

supply Probability 500 600 700 800 900 Demand 0.2 500 22500 19500 16500 13500 10500 0.2 600 22500 27000 24000 21000 18000 0.4 700 22500 27000 31500 28500 25500 0.15 800 22500 27000 31500 36000 33000 0.05 900 22500 27000 31500 36000 40500

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