The automobile assembly plant you manage has a Cobb-Douglas production function

Question

The automobile assembly plant you manage has a Cobb-Douglas production function given by p = 10x^0.2 y^0.8

where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Assume that you maintain a constant work force of 130 workers and wish to increase production in order to meet a demand that is increasing by 100 automobiles per year. The current demand is 1200 automobiles per year. How fast should your daily operating budget be increasing? HINT [See Example 4.] (Round your answer to the nearest cent.)

= ? $ per yr

Explanation / Answer

dp/dt=100 (required)

P=1200

x=130

so y=?

1200=10*130^0.2*y^0.8

y=117.62 $

now dp/dt=10x^0.2 *0.8 *y^(0.8-1) dy/dt

100=10*130^0.2 *0.8 * 117.62^ (-0.2) dy/dt

dy/dt=12.25 $ per yr (ans)

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