Question

# Set up but do not solve the Linear Programming problem that would solve the following:

A city

council is planning to build several hotels along its beach-front. They will be of two types: convention-style, each with 200 rooms and each costing $75 million to build, and vacation-style, each with 50 rooms and each costing $40 million.

The city council wants to build . . .

- At least 15 hotels altogether;
- without exceeding its budget of $725 million;
- With at least two-thirds of the money it spends going to vacation-style hotels; and
- producing at most three-fourths as many convention-style hotel rooms as vacation-style.

How many hotels of each type should the council build in order to maximize the total number of hotel rooms?