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...
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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?

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