ACCA PM Syllabus C. Decision-making Techniques - Shadow Prices (Dual Prices) - Past Papers ^{4 / 5}

C Co uses material B, which has a current market price of $0·80 per kg. In a linear program, where the objective is to maximise profit, the shadow price of material B is $2 per kg. The following statements have been made:

(i) Contribution will be increased by $2 for each additional kg of material B purchased at the current market price
(ii) The maximum price which should be paid for an additional kg of material B is $2
(iii) Contribution will be increased by $1·20 for each additional kg of material B purchased at the current market price
(iv) The maximum price which should be paid for an additional kg of material B is $2·80

Which of the above statements is/are correct?
A. (ii) only
B. (ii) and (iii)
C. (i) only
D. (i) and (iv)

A linear programming model has been formulated for two products, X and Y. The objective function is depicted by the formula C = 5X + 6Y, where C = contribution, X = the number of product X to be produced and Y = the number of product Y to be produced.

Each unit of X uses 2 kg of material Z and each unit of Y uses 3 kg of material Z. The standard cost of material Z is $2 per kg.

The shadow price for material Z has been worked out and found to be $2·80 per kg.

If an extra 20 kg of material Z becomes available at $2 per kg, what will the maximum increase in contribution be?

A. Increase of $96
B. Increase of $56
C. Increase of $16
D. No change