Stockbroker Susan Drexler has advised her client as shown in the following

table:

Investment Cost $($thousands$)$ Expected Return $($annual $-$ thousands$)$

Andover Municipal Bond $$400$ $$35$

Hamilton City Bond $$1000$ $$100$

East Power and Light $$350$ $$30$

Nebraska Electric $$700$ $$65$

Southern Gas and Electric $$490$ $$45$

Manual Products Co$.$ $$270$ $$20$

Builders Paint Co$.$ $$800$ $$90$

Rest Easy Hotels Co$.$ $$500$ $$50$

The client agrees to this list but provides several conditions:

$1.$ No more than $$3,000,000$ can be invested.

$2.$ The money is to be spread among at least $5$ investments.

$3.$ No more than $1$ type of bond can be purchased.

$4.$ At least $2$ utility stocks must be purchased.

$5.$ At least $2$ regular $($non$-$utility$)$ stocks must be purchased.

Formulate this as a $0-1$ IP problem $($each investment all or nothing$)$ for Ms$.$ Drexler to maximize

expected return.