Question

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The area of a parking lot at an amusement park is 1310 square meters. A car requires 5 square meters and a bus requires 32 square meters of space. There can be at most 135 vehicles parked at one time. If the cost to park a car is $5.00 and a bus is $15.00, how many busses should be in the lot to maximize income?
a.24
c.15
b.111
d.23

Answer 1

• d. 23

Explanation:

Let the number of cars be x and buses be y

Then we have below inequalities as per given:

• 5x + 32y ≤ 1310
• x + y ≤ 135

It is easy to notice that cars occupy 6 times less area than buses but cost of parking is 3 times less. So we would need maximum number of cars and minimum number of buses to maximize income

Let's assume there are 135 cars and buses, then from the second inequality:

• x = 135 - y

Substitute it in the first one:

• 5(135 - y) + 32y ≤ 1310
• 675 - 5y + 32y ≤ 1310
• 27y ≤ 1310 - 675
• 27y ≤ 635
• y ≤ 635/27
• y≤ 23.5

The greatest number of buses is 23

Option D. 23 is correct