How to Find Optimal Input Combination for Ice Cream Production

a) How can we plot the isoquant for 320 ice cream cones per day?

What is the optimal combination of inputs needed to produce 320 ice cream cones per day?

Plotting isoquant for 320 ice cream cones per day

An isoquant is the curve that shows the different combinations of labor and capital that can be used to produce a particular level of output. In this case, we want to plot the isoquant for 320 ice cream cones per day.

So the production function is Q = 4LM and we know that we want Q = 320. So 320 = 4LM or LM = 80. This means that for 320 ice cream cones per day, the ice cream vendor must rent enough machines and hire enough workers such that the product of the two is 80. For instance, he could rent 4 machines and hire 20 workers or rent 2 machines and hire 40 workers, and so on. The different combinations of L and M that give us Q = 320 are the points on the 80-isoquant.

We can plot this isoquant on the graph as shown below:

Finding the optimal combination of inputs

The optimal combination of inputs is the combination that minimizes the cost of producing a given level of output. In this case, we want to produce 320 ice cream cones and we know that the wage rate per day is $30, and the ice cream machine rental per day is $150.