Question

1. Nick buys a second oven and estimates output, see table 2

Table 2. Brownie output and number of workers, two ovens

Workers	Brownie output
1	10
2	24.5
3	38.5
4	52
5	64.75
6	76.75
7	87.75
8	97.75
9	106.75
10	114.75

assume ingredients cost a dollar per brownie. Use this table to recommend the number of workers he should hire, and the output of cookies he should produce, for a wage of $21, $18, $13.50.

Answer 1

Consider the given problem here if the price of “brownie” is “$2.5”, => TR is given by “P*B”, where “B=total production of brownie”. Now, here there two inputs “worker” and “ingredients”. So, the “ingredient cost” is “$1 per unit of output” and the “worker cost” is wage. So, the “TC” is given by “W*L +1*B”, where “W=wage”, “L=numbers of worker hired” and “B=units of brownie produced”. Consider the following table shows the “TR” and “TC” for different level of wage.

So, here for “W=21” the maximum profit is given by “-6”, => here the optimum production is “brownie” and the optimum labor hiring is “1”. Similarly, for “W=18” the maximum profit is given by “2.63”, => here the optimum production is “brownie” and the optimum labor hiring is “8”. Now, finally for “W=13.5” the maximum profit is given by “38.63”, => here the optimum production is “brownie” and the optimum labor hiring is “9”.