A firm produces bicycles using two inputs: bicycle frames (F) and bicycle wheels (W). By definition, one bicycle has 2 wheels and 1 frame. One frame costs $75, and 1 wheel costs $50. The firm is currently producing 100 bicycles per month. If the price of wheels doubles to $100 each, the cost minimization of producing 100 bicycles is now $.

C(100) = (75 x 100) + (200 x 100) = $27,500

Explanation:

the initial cost function of producing bikes is:

C(x) = 75F + 100W

the initial cost to produce 1 bike = $75 + $100 = $175

if the cost of wheels increase to $100 each, then the cost function is:

C(x) = 75F + 200W

in this case, there is not much to calculate since every bicycle must have 1 frame and 2 wheels, that means that in order to produce 100 bicycles you will necessarily need 100 frames and 200 wheels. Labor is not considered in this cost function, so any cost minimization strategy is limited to using the minimum amount of parts:

C(100) = (75 x 100) + (200 x 100) = $27,500

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