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Question

A parking lot has 650 square meters of total space available. A car requires 7 square meters of space and a bus requires 32 sq. meters of space. Cars are charged $4.00 to park while buses are charged $9.50. The parking attendant can handle no more than 50 vehicles. How many of each type of vehicle should they accept in order to maximize their total income? What is this maximum income?

Answer 1

Let x be the number of cars of size 7 m² and y the number of buses of size 32m². 

 

What you have here is a linear programming problem.

 

The total number of vehicles is less than or equal to 50, so x + y ≤ 50.

 

You also know that both x and y cannot be negative: x ≥ 0, y ≥ 0. 

 

The income from parking these vehicles will be:

 

C = 4x + 32y.

 

You also know that the total space used is less than or equal to 650.

 

This means that 7x + 32y ≤ 650.

 

Putting it all together,

 

Maximize: C = 4x + 32y

Subject to: 7x + 32y ≤ 650

                x + y ≤ 50

                x ≥ 0, y ≥ 0.

 

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