CHEMCO operates two plants, A and B, which produce the same product. The capacit

Question

CHEMCO operates two plants, A and B, which produce the same product. The capacity of Plant A is 60,000 gallons while that of plant B is 80,000 gallons. The annual fixed cost of Plant A is $2,600,000 per year and the Variable cost is $32 per gallon. The corresponding values for Plant B are $2,800,000 and $39 per gallon. At present, Plant A is being operated at 35% of capacity and plant B is being operated at 40% of capacity.

a) What would be the total cost of production of Plants A and B?

b)What are the total cost and the average unit cost of the total output of both plants?

c)What would be the total cost to the company and cost per gallon if all production were transferred to plant A?

d)What would be the total cost to the company and cost per gallon if all production were transferred to Plant B?

Explanation / Answer

Annaul FC of Plant A (FCA) = $2600000 Annual FC of Plant B (FCB) = $2800000 Operating Capacity of A (OCA) = 35% of 60000 = 21000 gallons Operating Capacity of B (OCB)= 40% of 80000 = 32000 gallons Variable Cost in Plant A, VCA = $32 per gallon Variable Cost in Plant B, VCB = $39 per gallon (a) Total Cost of Production(TC) = Fixed Cost(FC) + Variable Cost (VC) TCA = FCA + VCA * OCA = 2600000 + 32 * 21000 = 3272000 TCB = FCB + VCB * OCB = 2800000 + 39 * 32000 = 4048000 (b) Total Cost of both plants = $3272000 + $4048000 = $7320000 Average unit cost = total cost/total units = 7320000/(21000+32000) = $138.113 (c) IF the 32000 gallons at plant B is to be transferred to plant A, plant A should produce 53000 gallons(less than its capacity 60000) So, TCA = FCA + VCA * (OCA+OCB) = 2600000 + 32 * 53000 = $4296000 Cost per gallon = 4296000/53000 = $81.06 (d) IF the 21000 gallons at plant A is to be transferred to plant B, plant B should produce 53000 gallons (less than its capacity 80000) So, TCB = FCB + VCB * (OCA+OCB) = 2800000 + 39 * 53000 = $4867000 Cost per gallon = 4867000/53000 = $91.83

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