Question

Page 3 of 16 2. Profit maximization for a manufacturing company: The production cost function for ABC Manufacturing Company is C(x) - 8000x + 200,000 (05XS 200) where x number of units produced. The revenue function, R(x), is: R(x) – 22,000x - 70x (a) Find the profit function, P(x) for this company. [10 points) P(x) = R(x)-[(x) 5 (22,000x - 70X?) - -8000x + 200,000 P(x)=-70 x?+14000 x -20900 PCx) = -70x2 + 1400U X - 700,000 (b) Determine the production level, x, that will maximize the profit for the company and calculate the maximum profit at this level. Use calculus; show your work. (10 points] PS when x= (c) Graph the profit function, P(x) that you found and label the maximum profit at the production level you calculated in (b) above. (Identify P..on your graph.) To points 700,000 P(x) -300,000 200

Answer 1

2. Profit maximization for a manufacturing company: The production cost function for ABC Manufacturing Company is C(x) = 8000x + 200,000 (OSX S200) where x-number of units produced. The revenue function, R(x), is: R(x) = 22,000 - 70x (a) Find the profit function, Pix) for this company. [10 points] P(x) = R(x) -C(x) = (22000x70x²). -8000x + 200,000 P(x)=-70 x? +1400D -2090 -70 X2 +14 ODU X - 700,ODD (b) Determine the production level, x, that will maximize the profit for the company and calculate the maxim profit at this level. Use calculus; show your work. [10 points] Sol : P (n) = -2013 + 140000 - 200,000 so, Plas = - 20X20 + 14000 I for maximeum profit. P'(n) = 0 , 20x20 + 14000 30 i 2= 14000 = 100 2002 P=$ 500,000 when x= 100 Now, p (n=100) = -20x108² +14000x100 - 200,000 = 500.000 (c) Graph the profit function, P(x) that you found and label the maximum profit at the production les you calculated in (b) above. (Identify P... on your graph.) 110 points) A Pon) 700,000 Graph of Oundratic P(x) egh -300,000 100 200