# Stuck on word problem

• Oct 15th 2009, 04:29 PM
tux31189
Stuck on word problem
1.A company in manufacturing a new digital watch can sell all it manufactures. The cost (in dollars) is given by C(x)=5000+2x, where the production output in one day is x watches. If production is increasing at 5 watches per day when production is 375 watches per day, find the rate of increase in cost.

2. A beverage company works out a demand function for its sale of soda and finds it to be x=D(p)=4200-28p

where x=the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic?
• Oct 15th 2009, 11:07 PM
Hello tux31189

Welcome to Math Help Forum!
Quote:

Originally Posted by tux31189
1.A company in manufacturing a new digital watch can sell all it manufactures. The cost (in dollars) is given by C(x)=5000+2x, where the production output in one day is x watches. If production is increasing at 5 watches per day when production is 375 watches per day, find the rate of increase in cost.

If we measure the time, $t$, in days, then to say that production is increasing at $5$ watches per day can be written as: $\frac{dx}{dt}=5$

We need the rate of increase in cost; that's $\frac{dC}{dt}$

And the Chain Rule tells us:

$\frac{dC}{dt}=\frac{dC}{dx}\times\frac{dx}{dt}=2\f rac{dx}{dt}$, given that $C=5000+2x$

$=2\times 5 = 10$ dollars per day, when $\frac{dx}{dt}=5$