0 Question 6 v l3 0/10 pts '0 2 GI A box with a square base and open top must have a volume of 97556 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 3:, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of 3).] Simplify [your formula as much as possible. A(:1:) ='\ ' Next, find the derivative, A'(m). A'(:1:) =i i Now, calculate when the derivative equals zero, that is, when A'(:c) = 0. [Hintz multiply both sides by 3:2 -] A'(:c) = 0 when a: = We next have to make sure that this value of :1: gives a minimum value for the surface area. Let's use the second derivative test. Find A"(:1:). W) =l i Evaluate A"(a:) at the m-value you gave above. NOTE: Since your last answer is positive, this means that the graph of 24(3) 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 9 v El" 0/8 pts '0 2 C A manufacturer has been selling 1350 television sets a week at $540 each. A market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week. a) Find the demand function p(3:), where a: is the number of the television sets sold per week. 1006) = i ' 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 121500 + 1803:, how should it set the size of the rebate to maximize its profit? Si 1 Check Answer 0 Question 10 v E.' 0/10 pts '0 2 G D Suppose a company's revenue function is given by R(q) = q3 + 200132 and its cost function is given by C(q) = 460 + 1613, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively. A) Find a simplified expression for the m_arginal profit function. (Be sure to use the proper variable in your answer.) MP(q) = i B) How many items (in hundreds) need to be sold to maximize profits? Answer: hundred units must be sold. (Round to two decimal places.) Check Answer 0 Question 11 v B 0/10 pts Use linear approximation, i.e. the tangent line, to approximate v3 125.1 as follows: Let f(:1:) = 3/5. The equation of the tangent line to x) at :1: = 125 can be written in the form 3; = ma: + b where m is: ' ' and where bis: ' ' Using this, we find our approximation for V3 125.1 is ' Check