Co(X)= 5+0.5X and R (x) = 7x- 1/2x 2 are derived respectively, and the formulas of marginal fixed cost and marginal revenue are obtained.

C'o(X)= 0.5，R'(X)=7-x，

When R'(X)=C'o(X)+C'(X), the profit is maximized.

7-X = 0.5+3+ 1/3X =》0 = 10.5-7+4X = & gt； X=7/8

2. The second problem requires integration, which is to find the definite integral value of each function dx from 20 to 50. The total cost function is the indefinite integral of C'(X)=5+ 1/2X +C(0), and the total revenue function is the indefinite integral of r' (x) =100-x.