Suppose the revenue in thousands of ringgit from the manufac

Suppose the revenue in thousands of ringgit from the manufacture of x units of one product and y units of another is R(x, y) = 6xy + 4x -x^2 and average cost of producing y units and v units are as follows: AC(x) = x, AC(y) = 2y^2. How many units of each product will produce maximum profit? A firm\'s unit capital and labor costs are RM2 and RM3, respectively. Given the production function Q = f(K, L) = 4LK + L^2. where K and L are number of units of capital and labor, respectively. Find the levels of capital and labor at which output is maximized when the total input costs are fixed at RM200.

Solution

profit = R(x,y) - AC(x) - AC(y) = 6xy + 4x - x^2 - x - 2y^2

= 6xy +3x - x^2 - 2y^2

for maximum profit

partial derivatives are zero

6x - 4y = 0

6y + 3- 2x = 0

7x = -3

x = -3/7