$5\mathrm{.}7.$ Mountain Movers

The Mountain Movers truck company has $$1,200,000$ to replace its fleet. The

company is considering three different truck types:

Type C is the improved model of type B$.$ It has sleeping space for one driver.

This reduces its carrying capacity to $18$ tons and increases the price to $$90,000.$

The company employs $150$ drivers every day, has $50$ overnight parking spaces, and

wishes to maximize the delivery capacity of its fleet $($in ton$-$mi$/$day$).$

$($a$)$ Define the selection of the trucks as an optimization problem. Explain the

decision variables, objective function, and constraints.

$($b$)$ What assumptions, if any, did you make in this problem?