Kanto market is supplied n thousands of crates of dalandan daily when it is sold at p pesos per crate and the supply equation is...

Question

pn - 3p - 100n - 100 = 0

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

We do implicit differentiation: pdn/dt + ndp/dt - 3dp/dt - 100dn/dt = 0; n = 5000, dn/dt = - 250.

To get prise we put n = 5000: 5000p - 3p - 500000 - 100 = 0; 4997p = 500100; p = 100.08.

Now we have: - 250·100.08 + 5000·dp/dt - 3dp/dt + 25000 = 0; 4997dp/dt = 20; dp/dt = $0.004 per day