Question

SECTION 3.4: EXERCISES 1.) Consider the section of these notes dealing with "Marginal Analysis for Maximum Profit." Show how this technique for maximizing profit is just a SDT on P(x). Hint: Remember that P(x) = R(x) - C(x). Now apply the SDT. 2.) Consider the section of these notes dealing with "Marginal Analysis Criterion of Minimum Average Cost." Show why this method does, in fact, minimize the average cost. Hint: In the spirit of marginal analysis, think of C'(x) as an approximation of the cost of the "next" item made. Then consider the cases when A(z) <C' () and A > C'(x). What can be said about whether or not A(z) is increasing or decreases at such values of s?

Answer 1

Z Solution: we know that perl= R(x)-CCXI $ lepo and also know that for maximum prodit P'calco differentiate 6 boch sides coilte & we get pixla R'(al-c'cal if pical zo, then R'(x)_c'exico R (a)= cal for maximum value pucalco So, P'cali R"cal- c'(alco =) R" (a)-c'calco -) R"Cap & Cºco some xoo ca 1,2- Hence, the maximum profit at ni P(x) = R(xi) - c(xi), some iz1,2-