Question

ME: GROUP NUMBER & GROUP 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(). 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(x) < C'(x) and A > C'(?). What can be said about whether or not A(z) is increasing or decreases at such values of c?

Answer 1

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. Differentiating P(x) twice with respect tox, we get p'ıx) = R (x) - c'(x) & P"(x) = R "(x)–c"(x) So, P(x) will be maximum, whan Plex=0& P"(x) Co it R'(x)~ C'(x)=0 ) R(x) =c'(x) and R"(x) <c"(x). 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(x) < C'(x) and A > C'(?). What can be said about whether or not A(x) is increasing or decreases at such values of c? C(x) Anergie Cost Acx) = Ácx) xc'(x) -C(x) - 5 (c'ex-CEN) A"cx** xc">9-2c'ex) – (*e'(x)_289). 2x A"(x)= x <"(x)-2xc-cx) –2x'(x)+2x CCX) x² 24 Son 24 c'exy Cx2 -(3<"(2) - 4x² e'lx)+2 x C6))/24 Critical rohe is fiven by : Alcxo=0 - ACX where A(x) celx), then A'(x) >0 94. Ax) is increasing & when & when Acx>> c'x') then Alex) ne Ak) is decreasing in this condition.