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Answer the following problems. Show your solution for every item. l. Suppose the cost function of a commodity is C(x) = 8x + 3 and the price function y = 24 4x where x is the number of units produced in thousands, find the following: a. Profit function b. Most profitable output c. Maximum profit d. Revenue at the most profitable output . Marginal revenue at the most profitable output f. Cost at the most profitable output 2. HC(x)= ixz + 3x + 67 is the total cost of producing x units of a particular commodity and p(x) = %(45 - x) is the price at which all x units will be sold. a. Use marginal cost to estimate the cost of producing the 21* unit. b. Find the actual cost of producing the 21% unit. c. Find the marginal revenue at x = 20. d. Find the actual revenue derived from the sale of the 21 unit. 3. Given: f(x) = x* 4x 4 10, find a. Critical Value/s b. Critical Point/s . Relative Maxima d. Relative Minima . Interval when f(x) is increasing f. Interval when f(x) is decreasing g. Point of Inflection/s h. Interval when f(x) is concave up i. Interval when f(x) is concave down J- Sketch the graph. Use a graphing paper