the production function is f(L, M)= 4L^1/2 M^1/2, where L is the number of units of labor and M is the number of machines used.If the cost of labor is $49 per unit and the cost of machines is $25 per unit, then the total cost of producing 7 units of output will be A)$122.50. B)$259. C)$175. D)$245. E)None of the above.

Question

Quizplus · Accepted Answer

The total cost of production is given by the sum of the cost of labor and the cost of machines. The cost of labor is $49 per unit, and the cost of machines is $25 per unit. The production function is f(L, M)= 4L^1/2 M^1/2, where L is the number of units of labor and M is the number of machines used. To produce 7 units of output, we need to find the values of L and M that satisfy the equation f(L, M)= 7. Substituting the given production function into the equation, we get 4L^1/2 M^1/2 = 7. Solving for L, we get L = 7/4M^1/2. Substituting this expression for L into the cost of labor equation, we get the total cost of labor as 49(7/4M^1/2) = 343/4M^1/2. Similarly, the total cost of machines is 25M. The total cost of production is the sum of the total cost of labor and the total cost of machines, which is 343/4M^1/2 + 25M. To minimize the total cost of production, we need to find the value of M that minimizes this expression. Taking the derivative of the total cost of production with respect to M, we get d(343/4M^1/2 + 25M)/dM = -343/8M^3/2 + 25. Setting this expression equal to zero and solving for M, we get M = 16. Substituting this value of M back into the expression for the total cost of production, we get the total cost of production as 343/4(16)^1/2 + 25(16) = $122.50.

The Production Function Is F(L, M)= 4L1/2 M1/2, Where L

The Production Function Is F(L, M)= 4L^1/2 M^1/2, Where L