Optimal Combination of Inputs for Ice Cream Production

What is the optimal combination of inputs for an ice cream vendor to produce 80 cones per day?

Given the production function Q = LM and marginal product relationships MPL = M and MPM = L, how can we determine the optimal combination of inputs?

Optimal Combination:

The optimal combination of inputs for the ice cream vendor to produce 80 cones per day at minimum cost is hiring 4 workers and renting 20 machines, resulting in a total cost of $3,330.

To find the optimal combination of inputs for producing 80 ice cream cones per day, we need to analyze the production function Q = LM, where Q represents the number of ice cream cones produced, L is the number of workers hired per day, and M is the number of ice cream machines rented per day.

The isoquant for 80 ice cream cones per day will show all the combinations of L and M that result in the production of 80 ice cream cones. We can calculate the optimal combination by utilizing the marginal product relationships MPL = M and MPM = L.

Given the wage rate per day = $30 and the ice cream machine rental per day = $150, we can set up the equation MPL/W = MPM/R to determine the optimal inputs. By solving this equation, we find that hiring 4 workers and renting 20 machines will minimize the cost while producing 80 ice cream cones.

Therefore, the optimal combination of inputs for the ice cream vendor is to hire 4 workers and rent 20 machines, resulting in a total cost of $3,330 to produce 80 cones per day.