Question $3(5$ marks$).$

Suppose that widgets can be produced using two different production techniques, A and $B.$ The following table provides the total input requirements for each of five different total output levels.

$Q=1Q=2Q=3Q=4Q=5$

Technology K L K L K L K L K L

A $,$

$\backslash$table$[[2,5,1,10,5,146,188]]$

B $,$

$\backslash$table$[[5,2,8,3,114,145,166]]$

a$.$ Assuming that the price of labor $(PL)$ is $$1$ and the price of capital $(PK)$ is $$2,$ calculate the total cost of production for each of the five levels of output using the optimal $($least cost$)$ technology at each level.

b$.$ How many labor hours $($units of labor$)$ would be employed at each level of output? How many machine hours $($units of capital$)?$

c$.$ Graph total cost of production as a function of output. $($Put cost on the $Y-$axis and output, $q,$ on the $x-$axis.$)$ Again, assume that the optimal technology is used.