Thread: minimizing cost

Suppose that a cost-minimizing firm's production function is given to be
Q = (20)*(M^0.5)*(W^0.5)
where M stands for the labor of men and W stands for the labor of women (Both of which are expressed in person-hours).
Suppose men receive $6 per hour and women receive $5.50 per hour. Moreover, suppose the firm uses 400 person-hours of W and 625 person-hours of M to produce 10,000 units of output.
Is this firm minimizing the cost of producing this given level of output? If not, explain what this firm should do?


How should i approach this question?

Originally Posted by 413

Suppose that a cost-minimizing firm's production function is given to be
Q = (20)*(M^0.5)*(W^0.5)
where M stands for the labor of men and W stands for the labor of women (Both of which are expressed in person-hours).
Suppose men receive $6 per hour and women receive $5.50 per hour. Moreover, suppose the firm uses 400 person-hours of W and 625 person-hours of M to produce 10,000 units of output.
Is this firm minimizing the cost of producing this given level of output? If not, explain what this firm should do?


How should i approach this question?

First the question needs some clarification.

M is the number of hours of man labour employed
W the number of hours of woman labour employed.

Production is Q, and that requires:

M=(Q/10000)625 ... (1)
W=(Q/10000)400 ... (2)

Cost:

C(Q)=6M + 5.5W ... (3)

Now the question appears to be:

Does Q = (20)*(M^0.5)*(W^0.5) minimise (3) subject to (1) and (2)?

I'm not sure that this makes any sense!

RonL