Question

Federal Rent-a-Car is putting together a new fleet. It is considering package offers from three car manufacturers. Fred Motors is offering 5 small cars, 5 medium cars, and 10 large cars for $500,000. Admiral Motors is offering 5 small, 10 medium, and 5 large cars for $400,000. Chrysalis is offering 10 small, 5 medium, and 5 large cars for $300,000. Federal would like to buy at least 700 small cars, at least 600 medium cars, and at least 700 large cars. How many packages should it buy from each car maker to keep the total cost as small as possible?

Fred Motors	packages
Admiral Motors	packages
Chrysalis	packages

Answer 1

Solution:

  

From the given data we need to solve minimum packages to be bought from

Fred motors , Admiral motors, Chrysails motors.

We can write Fred motors as = x

Admiral motors = y

Chrysails motors = z

Given data is

Cars	x	y	z	Needed
Small	5	5	10	700
Medium	5	10	5	600
Large	10	5	5	700
Cost	$5,00,000	$4,00,000	$3,00,000

Then we write

5x + 5y + 10z >700 -------(1)

5x + 10y + 5z >600--------(2)

10x + 5y + 5z > 700-------(3)

By adding the three equations then we get

20x + 20y + 20z > 2000

Then x + y + z > 100--------(4)

Multipiy (4) with 5 then we get (5)

5x + 5y + 5z >500--------(5)

(1) - (5) then we get

5z = 200

z = 40

now (2) - (5)  

5y = 100

y = 20

then (3) - (5)

5x = 200

x = 40

Fred motors x = 40 Admiral motors y = 20 Chrysails motors z = 40

Total cost as small as possible is

= (40 * $5,00,000) + (20 * $4,00,000) + (40 * $3,00,000)

Total cost as small as possible = $40,000,000