You are responsible for managing a $$30,000$ account, some of which must be held as cash to cover current payables, some of which could be invested at somewhat higher risk to earn somewhat higher returns. Linear programming can be used to help decide how much should be held as cash and how much should be invested. The risks and returns are as follows:

cash

investment

return

$\mathrm{.}01$

$\mathrm{.}05$

risk

$\mathrm{.}01$

$\mathrm{.}04$

You must keep at least $$10,000$ as cash to cover payables. You would like to see a return of at least $$500.$ You want to minimize the total risk.

Draw a graph to represent the set of feasible alternatives

Compute the risk and return for each feasible corner on your graph.