Linear Programming

[troublemaker676]

The available parking area of a parking lot is 600 square meters. A car requires 6 square meters of space, and a bus requires 30 square meters of space. The attendent can handle no more than 60 vehicles.

(a) Let x represent the number of cars and let y represent the number of buses. Write a system of inequalities to represent the number of cars and buses that can be parked on the lot.

(b) If the parking fees are $2.50 for cars and $7.50 for buses, how many of each type of vehicle should the attendent accept to maximize income? What is the max. income?

I'm not sure if these equations are right for part (a)

6x+30y is less than or equal to 600

x+y is less than or equal to 60

x is greater than or equal to 0

y is greater than or equal to 0

Can someone check if these are right or not?

And what would my function befor the profit in terms of x and y?

f(x,y)=2.50x+7.50y

Once I know if the function and the equations are right i will be able to graph and solve. Any help is greatly appreciated.

And how do you do greater than/less than equal signs?

 

[rahian2k]

[deleted]

 

[troublemaker676]

Thanks for your help, I had no problem getting the answer.

 

[rahian2k]

[deleted]

 

[tkhunny]

This is really a subset of linear programming known as Integer Programming. You have nicely that cars can't be negative. It is only by luck (or deliberate problem design) that you managed integer solutions. Also, for an extremely practical point of view, one must know the precise shape of the parking area and cars and buses. If your integer solution means you have to bend a bus around a corner, you will have difficulty achieving that solution. As it stands, it is a nice problem for starters, but there is MUCH more to come. No need for boredom well into the future.