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
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
【参考答案及解析】
By definition, a shadow price is the amount by which contribution will increase if an extra kg of material becomes available. 20 × $2.80 = $56.
By definition, a shadow price is the amount by which contribution will increase if an extra kg of material becomes available. 20 × $2.80 = $56.