A market is supplied n thousands of crates of watermelons daily when it is sold at d dollars per crate and the supply equation is dn - 3d - 100n - 100 = 0.

Question

If the daily supply is decreasing by 250 crates per day, at what rate is the price changing when the daily supply is 5000 crates?

Answer 1

dn - 3d - 100n -100 = 0

Solving for d:

d = 100(n+1)/(n-3)

Taking the derivative of the original equation with respect to t:

d'n + n'd -3d' -100n' = 0

Solving for d':

d' = (100-d)n'/(n-3)

When n = 5 thousand and n' = -250 crates per day = -.25 thousand crates per day

d = 100(5 + 1)/2) = $300

d' = (100-300)(-.25)/2 = $25 per day