# Maximum Minimum Problem: Vehicle Parking Lot

by Andrew
(New York)

Need Assistance

Up to 6000 square meters of land is available to build a parking lot for cars and small trucks. The local government has stipulated five conditions that must be met before the project can be put before the planning committee for approval.
a. There must be at least 50 spaces for trucks.
b. each car must be allocated a minimum space of 15 sq meters.
c. each truck must be allocated a minimum space of 30sq meters
d.the parking lot must have at least twice as many spaces for cars as for trucks
e. cars must be charged \$2 per hr and trucks \$5 per hr.

1. what is the largest number of vehicles the parking lot could hold?
2. What number of car spaces and truck spaces will actually be provided in order to generate maximum revenue when the lot is full?

### Comments for Maximum Minimum Problem: Vehicle Parking Lot

 Sep 20, 2011 Maximum Minimum Problem - Vehicle Parking Lot by: Staff ------------------------------------------------------------------- Part II 2. What number of car spaces and truck spaces will actually be provided in order to generate maximum revenue when the lot is full? Each Car requires 15 sq meters of space Each Truck requires 30 sq meters of space cars must be charged \$2 per hr trucks must be charged \$5 per hr Every truck will require the same space as two cars. However every truck will generate more income than 2 cars. Every 2 cars generate an hourly revenue of \$4 per hour Every truck generates an hourly revenue of \$5 per hour Therefore maximum income will be achieved by maximizing the number of trucks and minimizing the number of cars. T = number of trucks T_max = The maximum number of trucks = unknown C = number of cars Since the parking lot must have at least twice as many spaces for cars as for trucks C_min = 2 * T_max C_min = minimum number of cars = unknown = 2 * T_max 6,000 sq meters = (T_ max) * 30 sq meters per truck + (C_ min) * 15 sq meters per car 6,000 sq meters = (T_ max) * 30 sq meters per truck + (2 * T_max) * 15 sq meters per car 6,000 = (T_ max) * 30 + (2 * T_max) * 15 6,000 = 30(T_ max) + 30(T_max) 6,000 = 60(T_ max) 6,000 / 60 = 60(T_ max) / 60 6,000 / 60 = (T_ max)* (60 / 60) 100 = (T_ max)* (60 / 60) 100 = (T_ max)* (1) 100 = (T_ max) T_ max = 100 truck spaces C_min = 2 * T_max C_min = 2 * 100 C_min = 200 car spaces the answer to question 2): 100 truck spaces, 200 car spaces Thanks for writing. Staff www.solving-math-problems.com

 Sep 20, 2011 Maximum Minimum Problem - Vehicle Parking Lot by: Staff Part I The question: by Andrew (New York) Need Assistance Up to 6000 square meters of land is available to build a parking lot for cars and small trucks. The local government has stipulated five conditions that must be met before the project can be put before the planning committee for approval. a. There must be at least 50 spaces for trucks. b. each car must be allocated a minimum space of 15 sq meters. c. each truck must be allocated a minimum space of 30 sq meters d. the parking lot must have at least twice as many spaces for cars as for trucks e. cars must be charged \$2 per hr and trucks \$5 per hr. 1. what is the largest number of vehicles the parking lot could hold? 2. What number of car spaces and truck spaces will actually be provided in order to generate maximum revenue when the lot is full? The answer: ------------------------------------------------------------------- 1. what is the largest number of vehicles the parking lot could hold? Available area = 6,000 sq meters Each Truck requires 30 sq meters of space Each Car requires 15 sq meters of space Every truck will require the same space as two cars. The maximum number of vehicles = minimum number of trucks + maximum number of cars. T = number of trucks T_min = The minimum number of trucks = 50 C = number of cars C_max = maximum number of cars = unknown 6,000 sq meters = (T_min) * 30 sq meters per truck + (C_max) * 15 sq meters per car 6,000 sq meters = 50 * 30 sq meters per truck + (C_max) * 15 sq meters per car 6,000 = 50 * 30 + (C_max) * 15 6,000 = 1500 + (C_max) * 15 6,000 = 1500 + 15(C_max) 6,000 - 1500 = 1500 - 1500 + 15(C_max) 4500 = 1500 - 1500 + 15(C_max) 4500 = 0 + 15(C_max) 4500 = 15(C_max) 4500 / 15 = 15(C_max) / 15 4500 / 15 = (C_max) * (15 / 15) 300 = (C_max) * (15 / 15) 300 = (C_max) * (1) 300 = C_max largest number of vehicles the parking lot could hold = minimum number of trucks + maximum number of cars. largest number of vehicles the parking lot could hold = 50 trucks + 300 cars largest number of vehicles the parking lot could hold = 350 vehicles (total the answer to question 1): 350 vehicles -------------------------------------------------------------------