Question

I have two problems that I can't figure out for my test review...

1. Productivity: Because a new employee must learn an assigned task, production will increase with time. Suppose that for the average new employee, the rate of performance is given by dN/dt=1/2?(t+1) where N is the number of unity completed t hours after beginning a new tak. If 2 units are completed afer 3 hours, how many units are completed after 8 hours?

2.Suppose that the marginal cost for a product is MC=60?(x+1) and its fixed cost is $340.00. If the marginal revenue for the product is MR=80x, find the profit or loss from production and sale of a) 3 units and b) 8 units

the question mark in prob. 2 for the Marginal Cost is supposed to be a square root sign...sorry!

I assume the ? in the first is sqrt also.

dN/dt=1/2 sqrt (t+1)
N= INT above= 1/3 (t+1)^3/2 + C


2= 1/3 (4)^3/2 + C or C= 2-8/3 check that.

THen solve for t=8

2)
Marginal cost=dC/dx
Marginal revenue=dR/dx

Profit=INT MR dx - INT MC dx + FC

Profit= INT 80x dx -INT 60sqrt(x+1)dx + FC