Minimize Q =5x2 + 3y , where x+ y =8. XE y= (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)Find the maximum prot and the number of units that must be produced and sold in order to yield the maximum prot. Assume that revenue, R(x), and cost, C(x), of producing x units are in dollars. Rtx) = 3x. C(x) = 0.05:? + 0.2x+10 What is the production level for the maximum prot? units Raggs, Lid. a clothing firm, determines that in order to sell x suits, the price per suit must be p = 160 -0.5x. It also determines that the total cost of producing x suits is given by C(x) = 5000 + 0.75x-. a) Find the total revenue, R(x). b) Find the total profit, P(x). c) How many suits must the company produce and sell in order to maximize profit? d) What is the maximum profit? e) What price per suit must be charged in order to maximize profit? a) R(x) =Let R(x), C(x). and P(x) be, respectively, the revenue, cost, and prot, in dollars. from the production and sale of x items. If R(x) = 7x and C(x) = 0.003x2 +1.?x + 50, nd each of the following. a] PM b) R[100),C[100),end Pace) 0] R'(x), 013:), and P'(x) d) when), c1100), and W100) a] P(x) = Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.006x* + 0.03x* + 0.4x. Currently, Pierce sells 50 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 55 lawn chairs were sold each day? c) What is the marginal revenue when 50 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(51), R(52), and R(53). a) The current revenue is $Assume that C(x) is in dollars and x is the number of units produced and sold. For the totalccsi function C(x) = 0.0'lx2 + 0.5: +20, nd :50 and C'()() when x=90 and x = 1. ac=$|: (Simplify your answer. Type an integer or decimal rounded to tum decimal places as needed.) Assume that Rm is in dollars and x is the number of unils prod used and sold. For the totalrevenue function R()() = 7x, nd AR and R'(x] when x = 30 and Ax = 1' E) &R = 5 (Simplify your answer.) \f18x + 800 The average cost for a company to produce x units of a product is given by the function A(x) = X . Use A (x) to estimate the change in average cost as production goes from 200 units to 201 units. The change in average cost is approximately | dollars.Find Ay and f'(x)Ax for y = f(x) = 3x", x=4, and Ax =0.04. Ay = (Round to four decimal places as needed.)