In: Advanced Math
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?
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