Suppose you manage a plant that produces engines by teams of workers using assem

Question

Suppose you manage a plant that produces engines by teams of workers using assembly machines. The technology is summarized by the production function Q = 4KL where Q is the number of engines produced per week, K is the number of assembling machines, and L the number of labor teams. Each assembly machine rents for r = $12,000 per week and each labor team costs w = $3,000 per week. Total engine costs are given by the cost of labor teams and assembling machines plus $2,000 per engine for raw (component) materials. Your plant currently has a fixed installation of 10 assembly machines as a part of its design.

Explanation / Answer

Q = Number of engines produced per week

K = Number of assembly machines = 10

L = Number of labour teams

r = rent for each assembly machine per week = $12000

w = cost of each labour team per week = $3000

each assembly line have one team for the production. So the total number of team involved will be 10.

So Q= 4KL

Q = 4*10*10 = 400

so the total number of engines produced will ve 400.

cost of engine is sum of r, w & $2000

so according to this

Cost of each engine will be = 12000+3000+200 = $15200

cost involved each week = $15200 * 400 = $6080000

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