Question

In: Advanced Math

A manufacturer of projection TVs must ship a total of at least 1000 TVs to its...

A manufacturer of projection TVs must ship a total of at least 1000 TVs to its two central warehouses, x to the first warehouse and y to the second warehouse. Each warehouse can hold a maximum of 750 TVs. The first warehouse already has 150 TVs on hand, whereas the second has 50 TVs on hand. It costs $10 to ship a TV to the first warehouse, and it costs $15 to ship a TV to the second warehouse. How many TVs should be shipped to each warehouse to minimize cost?

Expert Solution

Variable Declaration:

Let,

x1= Number of TV's shipped to the first warehouse

x2= Number of TV's shipped to the second warehouse

Objective Function:

For cost minimization,

Min z=10x1+15x2

Constraints:

x1+x2>=1000

x1<=750-150 i.e.x1<=600

x2<=750-50 i.e. x2<=700

For non-negativity constraints,

x1,x2>=0

LPP: (Graphical Method)

Red: x1 + x2 >= 1000
Green: x1 <= 600
Blue: x2 <= 700

600 number of TV's shipped to the first warehouse.

400 number of TV's shipped to the second warehouse.

400

Colby Messinger answered 8 months ago

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