Given revenue and cost functions R(q) = 70q - 0.3q2 and C(q) = 13q + 550, find the marginal profit at a quantity of 13 items. The marginal profit is $ per item. (Round to two decimal places.)Solution : = Given that , The revenue and cost functions are R ( 9 ) = 70 9 - 0. 392 c ( q ) = 139 + 550 we have profit = ( Revenue - Cost ) . Then the profit function is given by P ( 9 ) = R (9 ) - c (q ) = 709 - 0. 392- 139- 550 ByOf2 = - 0. 39 + 579-550 .. P (9 ) = - 0.392+ 579 - 550 3 The marginal profit , p' ( 9) is given by p' (9 ) = da [ P (9)] d ( -0.39 + 579- 550 ) [BY 3 = ( - 0.3 ) . 2. 9 +57. 1.9' -Lo : dy ( 97) = n. q2-1) do (C) =0for any constant C . . = - 0.69+57 ( :9' = 90 =1) p' ( 9 ) = - 06 9+57 At a quantity of 13 items, 9 = 13 " . The marginal profit of a quantity of. 13 items is given by p1 ( 13 ) = (:0.6 ) x 13 + 57 (By @ ) = 57 - 7.8 = 49 . 20 . . pt ( 13 ) = 49.20 " . The marginal profit is $ 49 .20 per item