# Math Help - Stuck on word problem

1. ## 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?

2. Hello tux31189

Welcome to Math Help Forum!
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 $\frac{dx}{dt}=5$

Grandad