a rnt-a-truck company

Question

a rent-a-truck company plans to spend $14 million on new vehicles. a van costs $45,000, a small truck costs $70,000, and a large truck costs $60,000. statistics show that they will need twice as many vans as small trucks. how many of each type of vehcle can they buy?

Answer 1

The problem addresses the ratio of vans to small trucks but nothing about  how many large trucks to vans or small trucks.  So lets assume he wants at least 1 large truck for every small truck purchased.  And if we let x = to the number of small trucks purchased, we have twice as many vans as small or large trucks, therefore, we have sufficient info to do the calculation.  The first run through will establish preliminary #'s of each type of vehicle, then we can check to see if he can buy one or two additional vehicles.  The first number gives us only the number of blocks of 4 vehicles he can buy.  After determining the price of x blocks of 4 vehicles at $220,000 amounts to we can subtract that value from the $14,000,000 to see how many additional vehicle can be purchased.

 

the owner has $14,000,000 to purchase 2*$45,000*x vans + x*$70,000 SmTrks + x*$60,000 Lg Trks 

 

Multiply through and gather all of the x's

 

                         $14,000,000=$90,000x + $70,000x + $60,000x = $220,000x

 

                                              x = $14,000,000/$220,000 = 63 vehicles

 

                  Preliminary total cost of vehicles = $45,000*2*63 + $70,000*63 + $60,000*63=

 

                                                                $5,670,000 + $4,410,000 + $3,780,000 = $13,860,000

 

                  Therefore, the owner has an additional $14,000,000 - $13,860,000 = $140,000 to purchase more

                  vehicles.  He can either purchase 3 more vans @ $45,000 = $135,000 or another van and large truck

                  which would amount to $45,000 + $60,000 = $105,000, or another van + a small truck which would

                  amount to $45,000 + 70,000 = $115,00.  Assuming he picks 1 van + 1 lg truck the total

                  mix of vehicles he would be purchasing would be as follows:

 

                                    Vans 63*2 +1 = 127 @ $45,000 Ea =  $5,715,000

                                     Sm Trks             63 @ $70,000 Ea =  $4,410,000

                                    Lg Trks 63 + 1 =  64 @ $60,000 Ea =  $3,840,000

                                                               Total Cost           =$13,965,000

                                      After the purchase he would have $35,000 left.