RE Marginal and average cost Suppose? the cost of producing ?x? lawnmowers is C?(? ?) = ?0.02x + 400?x? + 5000. a.? Determine the average and marginal costs for ?x? = 3000 lawnmowers. b.? Interpret the meaning of your results in part (a).

Solution Step 1 2 Let the cost of prod cing lawnmowe rs is ( ) = .02x + 400x + 5000. (a)The average cost is given by c(x) c(x) 2 x x = c= 0.02x + x00x + 5000. 5000 =0.02x+400+ x Hence the average cost for x=3000 is c(3000)=0.02(3000)+400+ 3000 = $ 341.67 Step 2: The marginal cost is given by c’(x)= (c(x)) dx = dx( 0.02x + 400x + 5000.) =(0.02(2x)+400) =(-0.04x+400) The marginal cost at x=3000 is c’(3000)=(-0.04(3000)+400) =$280