The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x)=x (3'}:2 +6le} , where x is the amount of cheese sold, in hundreds of pounds. The \"profit is ~ $80 when no cheese is sold. a. Find the profit function. b. Find the profit from selling 300 pounds of Brie cheese. a. Find the profit function. P(x)= | b. Find the profit from selling 300 pounds of Brie cheese, The profit from selling 300 pounds of Brie cheesa is | |. X , where x is the number of units produced. A company has found that the marginal cost (in thousands of dollars) to produce x central air conditioning units is C'(x) = 4x +e (a) Find the cost function, given that the company incurs a fixed cost of $10,000 even if no units are built. (b) The company will seek a new source of investment income if the cost is more than $18,000 to produce 5 units. Should they seek this new source? D (a) What substitution should be used to determine the cost function? Use the quantity as the substitution, u= so thatdu = [L D dx. The cost function is C(x) = |_] (b) Therefore, the cost of producing 5 units is sr] s0 the company Vl seak a new source of investment income. (Round to the nearest dollar as needed.) Find the area between the following curves. x=-5x=1,y=e*,andy=1-* The area is |:| (Type an exact answer in terms of e.) Suppose a company wants to introduce a new machine that will produce rate of annual savings (in dollars) given by the function $'(x), where x is the number of years of operation of the machine, while producing a rate of annual costs (in dollas) given by the function C'(x) b S=m-, C'(x)=il+x