A firm operates two plants. Plant A has a fixed cost of $£200{,}000$ and a variable cost of $£5$ per unit, with a maximum capacity of $30{,}000$ units. Plant B has a fixed cost of $£120{,}000$ and a variable cost of $£8$ per unit (no capacity limit). The market demand is $50{,}000$ units.\n\n(a) Determine the production allocation between the two plants that minimises total cost and state the minimum total cost.\n(b) If a per‑unit environmental tax of $£2$ is imposed on output from Plant B only, re‑evaluate the optimal allocation and the new total cost.

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Initial allocation: 0 units at Plant A, 50,000 units at Plant B; total cost £520,000. After tax: same allocation; total cost £620,000.

Gce Model Questions Vol1 2019 Economics Question 22

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