1) A commodity’s cost to produce is: C(x)=5000+70x+0.05x^2. What is the average rate of change from x=100 to x=105? and from x=100 to x=101? And the instantaneous rate of change when x=100
2) A pair of jeans’ marginal cost is C'(x)=0.003x^2+0.08x+3. What is C'(100)? I came up with 11.0009 but was told that was wrong…
3) The demand function for televisions is: p(x)= -1/10x + 550. 1000 tvs are sold a week at $450 but when there is a rebate of $10, an additional 100 are sold. In order to maximize revenue, how large should the rebate be? If the company’s cost is c(x) = 74000+120x, what should the size of the rebate be to maximize profit?
