Question

The total revenue function for a certain product is given by

The total revenue function for a certain product is given by R=630x dollars, and the total cost function for this product is C = 10,000+ 30x + x2 dollars, where x is the number of units of the product that are produced and sold. a. Find the profit function. b. Find the number of units that gives maximum profit. c. Find the maximum possible profit. a. P(x)= (Simplify your answer.) b. The number of units that gives maximum profit is x= c. The maximum possible profit is -

Answer 1

@ Given revenue function R = 630x and cost function Cz 10,000+ 30x+x2 a profit function P=R-C -)P: 630x - [10,000 +30% +x2] p. 6302 - 10,000 -30x -x? P: 630x - 30x - 19,000-X? pa | 6000 - 10,000-12 am. This is profit function 0 for finding maximum profit diff ce o wirton dp. d [60036 - 10,000-x} du dp = dr du . Good x-d 10,000 -day du du du dk du - dcont) :o) SdP: 600xl - 0 - 2x dr. 600 -24 -(2) du =) 600-20=0

- 2n- boo x = 600 2300 12=300 Again differentiate eg (2) wir to x adap lad (600-2x) duldu, dn dap d 600-224 du? In de d4 =0-2=-220 du? ei There is a manimam p at x = 300 .. The number of units that gives maximum profů x 300 ( for finding mau profit - put x = 300 in edD Prera 600X300-19.000-(300) Pmat : 180000-19.000-9 gove Pman 170 000-90,000 Pman=180,000) an. i The mani mum profit ů $180,000