Hard2 marksShort Answer

ACCA · Question 23 · Shadow Pricing

Section B - Case 2: BioNutri

BioNutri manufactures two specialized nutritional supplements: Alpha and Beta. Both products require processing on a specialized mixing machine. The machine is available for a maximum of 1,200 hours per month.

Product details:
Alpha: Selling price $50, Variable cost $30, Machine hours per unit: 2 hours. Maximum demand: 400 units.
Beta: Selling price $70, Variable cost $40, Machine hours per unit: 4 hours. Maximum demand: 300 units.

BioNutri has the opportunity to rent an additional identical mixing machine. What is the shadow price (maximum premium per hour) BioNutri should be willing to pay for one additional machine hour? (Enter the number only).

How to approach this question

The shadow price is the contribution generated by one additional unit of the limiting factor. Since Alpha's demand is fully met, an extra hour would be used to make more Beta.

Full Answer

In the optimal plan, demand for Alpha is fully satisfied (400 units). Demand for Beta is only partially satisfied (100 out of 300 units). Therefore, any additional machine hours would be used to produce more Beta. The contribution per machine hour for Beta is $7.50. This is the shadow price—the maximum premium over the normal variable cost BioNutri should pay for an extra hour.

Common mistakes

Stating $10 (the contribution of Alpha), forgetting that Alpha's demand is already capped.

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