# Thread: Calculus - Cost & Production applied problems

1. ## Calculus - Cost & Production applied problems

I have benn tackle with the following question for an hour but I still don't have a clue. All I got after an hour is Cost = 30r + 50n (Don't know if this is right as well).

Q:
Gym Sock Compant manufactures cotton athletic socks. Production is partially automated through the use of robots. Daily operating cost amount to $50 per labourer and$30 per robot.

The number of pairs of socks the company can manufacture in a day is given by x=50(n^0.6) (r^0.4) (A Cobb Douglas production formula), where x is the number of pairs of socks that cn be manufactured by N labourers and R robots.

Assuming that the compant wishes to produce 1000 pairs of socks per day at a minimom cost, how many labourers and how many robots should it use? You will need to formulate a cost function. Express your cost function as a function of robots, r, and continue from there.

Your answers for robots and labohrers will turn out to be fractional numbers. But you do not want fractional number of people or robots, naturally, so you will need to round your answers to interger values for r and n. Choose the most economical integer values, yet still satisfying the requirement of producing at least 1000 pairs of socks.

Thanks a lot!

2. ## Re: Calculus - Cost & Production applied problems

$\displaystyle 1000 = 50N^{0.6}R^{0.4}$

$\displaystyle 20 = N^{0.6}R^{0.4}$

solve for N in terms of R, then substitute for N in your correct cost equation ...

$\displaystyle C = 30R + 50N$

... then minimize Cost w/r to R