Make two problems on the application of definite integrals in business and economics. The picture is the basis for the tutor.

PS gain per unit XO Lowest price Quantity Example 1. If the supply function is y = (x + 2)2 and the price is Yo = 25, Find the producers surplus using two different methods. (0,25) (3,25)-7 70 14. PiS my=(x+2)2 V(-2 5) for my: 1 7:0 my - 14 (-2,0) Ax X 25 = (71 7) 2 743 X53 Solution PS = XoYo - fo f(x)dx PS = (3) (25) - S2(x + 2)2dx PS = (3) (25) - S2 (x+ 2)2dx PS = 75 -14(x +218 8 75' PS = 75 - = (125) + 1 (8) PS = 75 - 39 PS = 36 Alternative Solution YoPS = (125) - 50 - (8)+8 PS = 36 5 Example 2 The Quantity demanded and the corresponding price under pure competition are determined by the demand and supply functions y = 16 - x2 and y = 4 + x respectively. Determine the corresponding producer's surplus. - (y- 14) (0,16) N y-16-x (p 14) PS (3.7) 27 ( 7 ., 45 ) co.4) 7= 414 (-4.0) (4.0) (3,0) 6 Solution Equating the right sides of y = 16 - x2 and y = 4 + x to solve for the point of intersection we have, 16-x2 = 4+x x2 + x - 12 = 0 (x + 4)(x - 3) = 0 x+4 =0 x - 3 =0 x =4 x =3 If Xo = 3 then yo = 7 Solving for PS we have, PS = XoYo - *of(x)dx