Question

TV Circuit has 30 large-screen televisions in a warehouse in Erie and 60 large-screen 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 $17 to ship from Pittsburgh to Blairsville and $24 to ship from Pittsburgh to Youngstown, whereas it costs $18 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.

from Pittsburgh to Blairsville televisions?

from Pittsburgh to Youngstown televisions ?

from Erie to Blairsville televisions ?

from Erie to Youngstown televisions?

Answer 1

Let x be the number of tvs shipped from Pittsburgh to Blairsville

So the number shipped from Erie to Blairsville is represented by 35 − x

Let y be the number shipped from Pittsburgh to Youngstown

So the number shipped from Erie to Youngstown is represented by 40 − y

So we have

(35 - x)+(40 - y) <= 30

45 <= x+y

From 60 large-screen televisions in a warehouse in Pittsburgh we have

x + y >= 60

Constraints:

Now draw these contraints on a graph

Points A(5,40), B(20,40), C(35,25),D(35,10)

Total shipping cost = 17x + 24y + 18(35-x) + 27(40 - y)

C(x) = 17x + 24y + 630 -18x + 1080 -27y

= -x -3y +1710

	Point	C(x)
A	(5,40)	1585
B	(20,40)	1570
C	(35,25)	1600
D	(35,10)	1645

So the minimum C(x) is at point B(20,40)

Answer:

from Pittsburgh to Blairsville televisions = 20

from Pittsburgh to Youngstown televisions = 40

from Erie to Blairsville televisions = 35-20 = 15

from Erie to Youngstown televisions = 40 - 40 =0