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 550 small cars, at least 500 medium cars, and at least 550 large cars. How many packages should it buy from each car maker to keep the total cost as small as possible

Answer 1

Answer:

a) X ( number of package bought from Fred motors ) = 30

   Y ( number of package bought from Admiral ) = 20

   Z ( number of package bought from Chrysalis ) = 30

b) The smallest total cost = $32,000,000

Explanation:

Given data :

cars types         x                     y              z                quantity needed

small                  5                    5             10                      550

medium             5                    10            5                       500

large                  10                   5             5                       550

cost              $500,000     $400,000  $300,000        

Note : x = number of package bought from Fred motors , y = Admiral motors ,  z = Chrysalis motors

The number of packages to be bought from each car manufacturer to keep total cost as small as possible

X ( number of package bought from Fred motors ) = 30

Y ( number of package bought from Admiral ) = 20

Z ( number of package bought from Chrysalis ) = 30

The smallest total cost = ( 30 * 500,000 ) + ( 20*400,000) + (30*300,000 )

                                      = $32,000,000

Attached below is the detailed solution