Question 1

The company’s profit function is as below:-

Π = 12PA + 16PB + 13PC

This function shows total amounts of A, B and C produced and sold at their respective prices.

Below are constraints within which production of A, B and C are limited:

6 PA + 12PB + 8PC   81,000

4 PA + 4PB + 6P≤ 32,400

3 PA + 2PB + 3P≤ 16,300

The problem can be stated as:-

Maximize 12PA + 16PB + 13PC

Subject to:-

6 PA + 12PB + 8PC   81,000

4 PA + 4PB + 6P≤ 32,400

3 PA + 2PB + 3P≤ 16,300

1. b) Excel Solver Calculation

1. c) Maximum profit which will therefore be gained is £16,200.
2. d) Based on the optimal production mix, all 8,100 minutes available for moulding have been used up, 27,000 minutes of trimming time remain unused and 12,250 minutes of packaging time remain unused.

Question 2

The optimal decision in EDCF Company is that which maximizes profit. Gross profit is obtained by subtracting costs from the selling price. The optimal decision is therefore the one with the highest gross profit. There are twelve decision options as shown in the decision tree diagram below.

Option I: Import, have tariff charged, advertise and have 300 sales. This option has a total cost of £2,825.80 and sales revenue of £6,000.00. The profit is therefore £3,174.20.

Option II: Import, have tariff charged, advertise and have 200 sales. This option has a total cost of £1450.80 and sales revenue of £4,000.00. The profit is therefore £2,549.20.

Option III: Import, have tariff charged, not advertise and have 300 sales. This option has a total cost of £810.80and sales revenue of £6000.00. The profit is therefore £5,190.00.

Option IV: Import, have tariff charged, not advertise and have 2 00 sales. This option has a total cost of £1,820.80 and sales revenue of £6000.00. The profit is therefore £4,179.20.

Option V: Import, no tariff charged, advertises and has 300 sales. This option has a total cost of £2,825.00 and sales revenue of £6,000.00. The profit is therefore £3,175.00.

Option VI: Import, no tariff charged, advertises and has 200 sales. This option has a total cost of £1450.00 and sales revenue of £4,000.00. The profit is therefore £2,550.

Option VII: Import, no tariff charged, not advertised and has 300 sales. This option has a total cost of £810.00 and sales revenue of £6000.00. The profit is therefore £5,200.00.

Option VIII: Import, no tariff charged, not advertise and have 2 00 sales. This option has a total cost of £1,820 and sales revenue of £6000.00. The profit is therefore £4,180.00.

Option IX: Manufacture, advertises and has 300 sales. This option has a total cost of £3,050.00 and sales revenue of £6,000.00. The profit is therefore £2,950.00.

Option X: Manufacture, advertises and has 200 sales. This option has a total cost of £1,500.00 and sales revenue of £4,000.00. The profit is therefore £2,500.

Option XI: Manufacture, no adverts and has 300 sales. This option has a total cost of £900.00 and sales revenue of £6,000.00. The profit is therefore £5,100.

Option X: Manufacture, no adverts and has 200 sales. This option has a total cost of £1,960.00 and sales revenue of £4,000.00. The profit is therefore £2,040.

From the twelve possible outcomes above the option with the highest payoff in the form of expected gross profit is Option III. The company is expected to make the most money if it imports, there is no tariff charge, they do not advertise and 300 items are sold.

Figure 1. Decision Tree – Importation Option

Figure 2.Decision Tree – Manufacturing Option.