I am having trouble with defining the variables and setting up the constraints.

Question

I am having trouble with defining the variables and setting up the constraints. This is how I've approached the problem so far:

let x = no. of packages purchased by the firm from MR1

y = no. of packages purchased by the firm from MR2

z = no. of packages purchased by the firm from MR3

Objective function = ?

Constraints = ?

A car rental company that operates all along the East coast intends to put together a fleet of small, medium, and large cars by purchasing them from three motor retail outlets in the form of packages that consist of a mixture of different sized cars. MR1, the first motor retail outlet, is offering packages that consist of 5 small cars, 5 medium cars, and 10 large cars, at a cost of S500.000 per package; MR2 is offering packages that consist of 5 small cars (no medium cars) and 5 large cars for $200,000 each; and MR3 is offering packages that consist of 10 small, 5 medium, and 5 large cars for $300,000 each. The rental company intends to put together a fleet that consists of at least 900 small cars, at least 350 medium cars, and at least 750 large cars, and intends to purchase at least half its packages from MR3. How many packages should the firm purchase from each retail outlet in order to minimize its costs?

Explanation / Answer

let x = no. of packages purchased by the firm from MR1

y = no. of packages purchased by the firm from MR2

z = no. of packages purchased by the firm from MR3

total number of packages = x+y+z

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