A short run production function of a competitive firm is given by Y= 6L^(2/3) where Y represents the units of output while L is the labour required. If Price (P)= 3 and Wage (W)= 6, how many units of labour (L) will the firm hire? I need help with this, thank you​

Economists often use a short-hand form for the production function: Q=f[L,K] Q = f [ L , K ] , where L represents all the variable inputs, and K represents all the fixed inputs.To determine the optimal capital-labor ratio set the marginal rate of technical substitution equal to the ratio of the wage rate to the rental rate of capital: K L = 30 120 , or L = 4K. Substitute for L in the production function and solve where K yields an output of 1,000 units: 1,000 = (100)(K)(4K), or K = 1.58.The production function is f(x1, x2) = x1/21x1/22. If the price of factor 1 is $12 and the price of factor 2 is $24, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? x1 = 2x2.There is no difference between fixed and variable factors of production. There are 3 stages namely, increased returns, constant returns, and decreasing returns, and no stage is considered best for the long run.Least Cost Rule: production at least cost requires the ratio of labor's marginal product to its price equals the ratio of capital's marginal product to its price. The amounts of labor and capital employed must be adjusted, all the while keeping output constant, until this condition is achieved.

Explanation: