I Question 6 v A box with a square base and open top must have a volume of 108000 ems. 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 3:, the length of one side of the square base. [Hintz use the volume formula to express the height of the box in terms of 3.] Simplify your formula as much as possible. 14(3) z" ' Next, find the derivative, A' (:13) A") =l ,l Now, calculate when the derivative equals zero, that is, when A'(a:) = 0. [Hintz multiply both sides by $2 -] 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".(m) A" Given the given cost function C(m) = 6450 + 650:]: + 1.13:2 and the demand function 13(3)) = 1950. Find the production level that will maximize profit. Check Answer Question 8 For the given cost function C(a) = 44100 + 600x + x2, First, find the average cost function. Use it to find: a) The production level that will minimize the average cost T= b) The minimal average cost Check Answer0 Question 9 v A manufacturer has been selling 1750 television sets a week at $420 each. A market survey indicates that for each $26 rebate offered to a buyer, the number of sets sold will increase by 260 per week. a) Find the demand function p(:c), where a: is the number of the television sets sold per week. pm =i 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 122500 + 1403:, how should it set the size of the rebate to maximize its profit? Si l Check