Question 1049004: I want the solution for this question with complete steps. Please help me.
Question: New York city has received a federal grant of $100million for improving public transportation. The funds are to be used only for the purchase of new buses, the purchase of new subway cars, or the repaving of city streets. Costs are estimated at $150,000per bus, $180,000per subway carand $250,000 per mile for the repaving. City officials want to determine different ways of spending the grant money.
a) Define the decision variables and write the equation which ensures complete expenditure of the federal grant.
b) If it has been determined that 100 buses and 200 new subway cars will be purchased, how many miles of city streets can be repaved?
C) If officials wish to spend all of the grant money on one type of improvement, what are the different possibilities?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let g = the federal grant.
let b = the number of buses.
let s = the number of subway cars.
let p = the number of miles of city streets to be paved.
you are given that g = 100,000,000
you are given that each bus costs 150,000.
you are given that each subway car costs 180,000.
you are given that each mile of city streets to be paved costs 250,000.
since you want to spend the total grant, then your equation becomes:
g = 150,000 * b + 180,000 * s + 250,000 * p
since g = 100,000,000, the equation becomes:
100,000,000 = 150,000 * b + 180,000 * s + 250,000 * p
if you assume b = 100 and s = 200, then the equation becomes:
100,000,000 = 150,000 * 100 + 180,000 * 200 + 250,000 * p
simplify this equation to get:
100,000,000 = 15,000,000 + 36,000,000 + 250,000 * p
combine like terms to get:
100,000,000 = 51,000,000 + 250,000 * p
subtract 51,000,000 from both sides of the equation to get:
49,000,000 = 250,000 * p
solve for p to get:
p = 49,000,000 / 250,000 = 196
if they buy 100 buses and 200 subway cars, then they will be able to pave 196 miles of city streets.
if they want to spend all of the grant money on one type of improvement only, then:
100,000,000 = 150,000 * b.
solve for b to get 666 and 2/3 buses which you would round down to 666 buses and have 100,000 left over.
100,000,000 = 180,000 * s.
solve for s to get 555 and 5/9 subway cars which you would round down to 555 subway cars and have 100,000 left over.
100,000,000 = 250,000 * p.
solve for p to get 400 miles of city streets that can be paved with nothing left over.
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