A manufacturer of projection TVs must ship a total of at least 1150 TVs to its two central warehouses. Each warehouse can hold a maximum of 760 TVs. The first warehouse already has 60 TVs on hand, whereas the second has 75 TVs on hand. It costs $39 to ship a TV to the first warehouse, and it costs $84 to ship a TV to the second warehouse. How many TVs should be shipped to each warehouse to minimize cost? Solution Let x be no of TV\'s shipped to A and y be no. of TV\'s shipped to B warehouses Given x+y >= 1150 x <= 760-60 i.e. x<=700 y <= 760-75 i.e. y<=685 Moreover x>=0 and y>=0 Plotting the above five regions in a graph paper,we get a triangular region with vertices (700,685),(700,450),(465,685) cost function is 39x+84y It is minimised for (700,450) Hence to minimize cost no.of TV\'s that to be shipped to first warehouse = 700 no.of TV\'s that to be shipped to second warehouse = 450.

1. A manufacturer of projection TVs must ship a total of at least 1150 TVs to its two central
warehouses. Each warehouse can hold a maximum of 760 TVs. The first warehouse already has
60 TVs on hand, whereas the second has 75 TVs on hand. It costs $39 to ship a TV to the first
warehouse, and it costs $84 to ship a TV to the second warehouse. How many TVs should be
shipped to each warehouse to minimize cost?
Solution
Let x be no of TV's shipped to A and y be no. of TV's shipped to B warehouses
Given x+y >= 1150 x <= 760-60 i.e. x<=700 y <= 760-75 i.e. y<=685 Moreover x>=0 and y>=0
Plotting the above five regions in a graph paper,we get a triangular region with vertices
(700,685),(700,450),(465,685) cost function is 39x+84y It is minimised for (700,450) Hence to
minimize cost no.of TV's that to be shipped to first warehouse = 700 no.of TV's that to be
shipped to second warehouse = 450