Question

An auto manufacturer sends cars from two plants, I and II, to dealerships A and B located in a mid-western city. Plant I has a total of 74 cars to send, and plant II has 70. Dealer A needs 79 cars, and dealer B needs 65. Shipping costs are $300 per car from plant I to dealer A, $130 per car from plant I to dealer B, $180 per car from plant II to dealer A, and $160 per car from plant II to dealer B. The manufacturer wants to limit total shipping costs to exactly $29,900. How many cars should be sent from each plant to each dealer

Answer 1

Total transportation cost = 23,750

Step-by-step explanation:

We can calculate how many cars should be sent from each plant to each dealer as follows

DATA

Plant 1 cars = 74

Plant 2 cars = 70

Demand

Dealer A needs 79 cars

dealer B needs 65

Shipping costs are

$300 per car from plant I to dealer A,

$130 per car from plant I to dealer B,

$180 per car from plant II to dealer A

$160 per car from plant II to dealer B.

limit total shipping costs to exactly $29,900

Start from the cheapest

$130 per car from plant I to dealer B.

$130 x 65 = 8,450

$180 per car from plant II to dealer A

$180 x 70 = 12,600

$300 per car from plant I to dealer A,

$300 x 9 = 2700

Total transportation cost = 8,450 + 12,600 + 2700

Total transportation cost = 23,750