Thread: Linear Program help

Hello, I'm stumped on this problem. Any help would be greatly appreciated Also a good explanation would be nice, considering I suck at math. Thanks!

The publicity director for Mercy Hospital is planning to
bolster the hospital’s image by running a TV ad and a radio ad. Due
to budgetary and other constraints, the number of times she can run
the TV ad (denoted by x) and the number of times she can run the
radio ad (y), is constrained to lie in the region shown below (the
region of feasible solutions is given the portion enclosed by the line
segments). The formula

A = 90000x+ 40000y

gives the total number of people reached by the ads. Find the maximum number

of people that can be reached running these ads. What

is the best mix for the number of television and number of radio ads
to run?

Originally Posted by Rob

Hello, I'm stumped on this problem. Any help would be greatly appreciated Also a good explanation would be nice, considering I suck at math. Thanks!

The publicity director for Mercy Hospital is planning to
bolster the hospital’s image by running a TV ad and a radio ad. Due
to budgetary and other constraints, the number of times she can run
the TV ad (denoted by x) and the number of times she can run the
radio ad (y), is constrained to lie in the region shown below (the
region of feasible solutions is given the portion enclosed by the line
segments). The formula

A = 90000x+ 40000y

gives the total number of people reached by the ads. Find the maximum number

of people that can be reached running these ads. What

is the best mix for the number of television and number of radio ads

to run?

With a linear objective to maximise/minimise we know that the maximum/
minimum lies on the boundary of the feasible region. Assuming the boundary
is a closed polygon we know in addition that the maximum/minimum is
realised at a vertex (in the degenerate case an entire edge will be optimal
but that still give two vertices where the objective is at its
maximum/minimum.

So if we evaluate the objective at each of the vertices of the feasible
region one where it takes its greatest value is an optimal point.

RonL