Determine the optimal production plan for the four-week period ending 30 June 20-新东方在线职业题库

Determine the optimal production plan for the four-week period ending 30 June 20X0, assuming that RAB is seeking to maximise the profit earned. You should use a linear programming graph, identify the feasible region and the optimal point and accurately calculate the maximum profit that could be earned using whichever equations you need.

考点：Chapter4Limitingfactoranalysis

Step 1 Define variables

Let a = number of type A projects

Let b = number of type B projects

Step 2 Establish objective function

Maximise contribution (C) = 580a + 620b, subject to the constraints below.

Step 3 Establish constraints

Qualified researchers time: 20a + 12b ≤ 1,344

Junior researchers time: 8a + 15b ≤ 1,120

Agreement for type A: a ≥ 20

Maximum for type B: b ≤ 60

Non-negativity: b ≥ 0

Step 4 Graphing the problem

Constraints

Qualified researcher time: if a = 0, b = 112

if b = 0, a = 67.2

Junior researcher time: if a = 0, b = 74.67

if b = 0, a = 140

Agreement for type A: graph the line a = 20

Maximum for type B: graph the line b = 60

Step 5 Define feasible region

Iso-contribution line

580a + 620b = 35,960 (where 35,960 = 58 × 62 × 10) goes through the points (62, 0) and (0, 58)

Step 6 Determine optimal solution

Find the co-ordinates of A

20a + 12b = 1,344 (1)

8a + 15b = 1,120 (2)

20a + 37.5b = 2,800 (3) (2) × 2.5

25.5b = 1,456 (3) – (1)

b = 57.10

20a + 685.20 = 1,344 substitute into (1)

a = 32.94

The profit-maximising mix of projects is 32.94 of type A and 57.10 of type B.

Profit for profit-maximising mix

Contribution from type A: 32.94 × $580 19,105

Contribution from type B: 57.10 × $620 35,402

Total contribution 54,507

Less: fixed costs (28,000)

26,507

多做几道

A public health clinic is the subject of a scheme to measure its efficiency and effectiveness. Among a number of factors, the 'quality of care provided' has been included as an aspect of the clinic's service to be measured. Three features of 'quality of care provided' have been listed.

(1) Clinic's adherence to appointment times

(2) Patients' ability to contact the clinic and make appointments without difficulty

(3) The provision of a comprehensive patient health monitoring programme

Required

(i) Suggest a set of quantitative measures which can be used to identify the effective level of achievement of each of the features listed.

(ii) Indicate how these measures could be combined into a single 'quality of care' measure.

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【论述题】

The absence of the profit measure in non profit seeking organisations causes problems for the measurement of their efficiency and effectiveness.

Required

(i) Explain why the absence of the profit measure should be a cause of the problems referred to.

(ii) Explain how these problems extend to activities within business entities which have a profit motive. Support your answer with examples.

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【论述题】

Compare and contrast the use of residual income and return on investment in divisionalperformance measurement, stating the advantages and disadvantages of each.

Division Y of Chardonnay currently has capital employed of $100,000 and earns an annual profit after depreciation of $18,000. The divisional manager is considering an investment of $10,000 in an asset which will have a ten-year life with no residual value and will earn a constant annual profit after depreciation of $1,600. The cost of capital is 15%.

Calculate the following and comment on the results.

(i) The return on divisional investment before and after the new investment

(ii) The divisional residual income before and after the new investment

Explain the potential benefits of operating a transfer pricing system within a divisionalised company.