TV Circuit has 30 largescreen televisions in a warehouse in

TV Circuit has 30 large-screen televisions in a warehouse in Erie and 60 largescreen televisions in a warehouse in Pittsburgh. Thirty-five are needed in a store in Blairsville, and 40 are needed in a store in Youngstown. It costs $18 to ship from Pittsburgh to Blairsville and $24 to ship from Pittsburgh to Youngstown, whereas it costs $20 to ship from Erie to Blairsville and $27 to ship from Erie to Youngstown. How many televisions should be shipped from each warehouse to each store to minimize the shipping cost? Hint: If the number shipped from Pittsburgh to Blairsville is represented by x, then the number shipped from Erie to Blairsville is represented by 35 x.

Solution

Let x be the number of televisions shipped from Pittsburg to Blairsville. Then the number of televisions shipped from Erie to Blairsville is 35 - x. The cost of shipping x televisions from Pittsburg to Blairsville is 18x and the cost of shipping 35 - x televisions from Erie to Blairsville is 20(35 - x). Thus, the total cost of shipping x televisions from Pittsburg to Blairsville and 35 - x televisions from Erie to Blairsville is 18x + 20(35 -x) = 700 - 2x. The cost of shipping cannot be negative, so the minimum value of 700 - 2x is 0. When 700 - 2x = 0, then x = 35. Thus 35 televisions would be shipped from Pittsburg to Blairsville and none from Erie to Blairsville. Now as regards Younstown, the requirement there is 40 televisions.The cost of shipping a television from Pittsburg to Youngstown is $ 24 while the cost of shipping a television from Erie to Youngstown is $ 27 which is higher than the cost of shipping a television from Pittsburg to Youngstown .Thus, to keep the cost minimum, all the remaining televisions, i.e. ( 60 -35) = 25 televisions should be shipped from Pittsburg to Youngstown. The balance requirement i.e. 40 - 25 = 15 televisions should be shipped from Erie to Youngstown. The result is summarised as under: