The marginal cost C' (x) and marginal revenue R' (x) are given by C' (x) = 20 +\(\frac{x}{20}\) and R' (x) = 30. The fixed cost is Rs.200. Determine the maximum profit.

The marginal revenue function (in thousands of rupees) of a commodity is 7+^e-0.05x where x is the number of units sold. Find the total revenue from the sale of 100 units (e^-5 = 0.0067)

The marginal cost function of a commodity in a firm is 2 + e^3x where X is the output. Find the total cost and average cost function if the fixed cost is Rs. 500.

Find the area of the region bounded by the curve y = 3 x² - x, X-axis and the lines between x = -1 and x= 1

Find the area of the region bounded by the parabola y² = 4x and the line 2x - y = 4.