Question

When a company produces and sells x thousand units per week, its total weekly profit is p thousand dollars, where p = 500x / 100+x2 . the production level at t weeks from the present is x=4+2t. find the marginal profit, dp/dx, and the time rate of change of profit, dp/dt. how fast (with respect of time) are profits changing when t=8?

Answer 1

Given t = 8
x = 4 + 2*8 => x = 20
that means company produces 20000 units/week

p = 500*20000/100+20000*2
so the total weekly profit is
p = 249.377 dollars