I Question 4 v 8 OH pt '0 2 G Details A box with a square base and open top must have a volume of 32000 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only m, the length of one side of the square base. [Hintz use the volume formula to express the height of the box in terms of 33.] Simplify your formula as much as possible. A(a:) 2" ' Next, find the derivative, A'($). A'(m) =l .' Now, calculate when the derivative equals zero, that is, when A'(m) = 0. [Hintz multiply both sides by x2 -] A'(m) = 0 when a: = We next have to make sure that this value of 3: gives a minimum value for the surface area. Let's use the second derivative test. Find A".(:c) A"(m) =l' i Evaluate A"(m) at the m-value you gave above. NOTE: Since your last answer is positive, this means that the graph of A(:c) is concave up around that value, so the zero of A'(m) must indicate a local minimum for A(m). (Your boss is happy now.) Check Answer 0 Question 3 v B 0/10 pts '0 2 G) Details A manufacturer has been selling 1300 television sets a week at $450 each. A market survey indicates that for each $17 rebate offered to a buyer, the number of sets sold will increase by 170 per week. a) Find the demand function p(a:), where .7; is the number of the television sets sold per week. pm = l J b) How large rebate should the company offer to a buyer, in order to maximize its revenue? Si J c) If the weekly cost function is 97500 + 150:5, how should it set the size of the rebate to maximize its profit? Sixl Check