The number of units x that consumers are willing to purchase at a given price p is defined as the demand function p=f(x). Suppose the cost of production is given by C(x)=4000- 40x + 0.02x2 and the demand function is p(x)= 50 -x/100. Find the unit price p that produces maximum profit. Find the number of items x for which production cost is minimum. Find the value of x for which average cost C- per item is minimum. (Hint: C- is minimum where its graph has a horizontal tangent line, so the derivative of C- is zero) When average cost C- is minimum, show that average cost and marginal cost are equal. Having produced 1000 items, approximate the additional cost of producing one more. Do the same for 5000 items.