W = $ 80 K = 5 P = $ 500 P x = $ 11,000 5 units of capital = 11,000 1 unit of capital = 2,200 Q = 2 ( 5 ) 1/2 ( L ) 1 / 2 Q = 4.47 ( L ) 1/2 MP L = 4.47 / L 1/2 MP L * Price = Wage ( 4.47 / L 1/2 ) * 500 = 80 L 1/2 = 500 * 4.47 / 80 L = 195.31 profit-maximization of labor usage Q = 2 ( 5 ) 1/2 ( 195.31 ) 1 / 2 Q = 62.5 Total Revenue = 500 * 62.5 = 31,250 Total Cost = 80 * 195.31 + 11,000 = 26,624.8 Max Profit of output = 31250 - 26624.8 = 4,625.2 1 Step-by-step explanation Generated by AI The question is asking for the profit-maximizing level of output and labor usage given the production function, wage rate, price per chair, and capital costs. Step 1: Calculate the cost of one unit of capital. The total cost of 5 units of capital is $11,000, so one unit of capital costs $2,200. Step 2: Substitute the value of K (capital) into the production function Q = 2(K)^1/2(L)^1/2. This gives Q = 2(5)^1/2(L)^1/2 = 4.47(L)^1/2. Step 3: Calculate the marginal product of labor (MP L) by taking the derivative of the production function with respect to L. This gives MP L = 4.47/L^1/2. Step 4: Set the wage equal to the marginal revenue product of labor (MP L * Price) to find the profit-maximizing level of labor. This gives (4.47/L^1/2) * 500 = 80, which simplifies to L = 195.31. Step 5: Substitute the value of L into the production function to find the profit-maximizing level