Question $1(8$pts$)$: Problem $57$ of Chapter $3,$ on Page $123$ of Winston book.

Transeast Airlines flies planes on the following route: L$.$A$.-$Houston$-$N$.$Y$.-$Miami$-$L$.$A$.$ The length $($in miles$)$ of each segment of this trip is as follows: L$.$A$.-$Houston, $1,500$ miles; Houston N$.$Y$.,1,700$ miles; N$.$Y$.-$Miami, $1,300$ miles; Miami$-$L$.$A$.,2,700$ miles. At each stop, the plane may purchase up to $10,000$ gallons of fuel. The price of fuel at each city is as follows: L$.$A$.,88!in$; Houston, $15$; N$.$Y$.,$ $$1\mathrm{.}05$; Miami, $95$d$.$ The plane's fuel tank can hold at most $12,000$ gallons. To allow for the possibility of circling over a landing site, we require that the ending fuel level for each leg of the flight be at least $600$ gallons. The number of gallons used per mile on each leg of the flight is

$1+(average$ fuel level $on$ leg $of$ fligh$\frac{t}{2},000)$

To simplify matters, assume that the average fuel level on any leg of the flight is $[($Fuel level at start of leg$)+($fuel level at end of leg$)]\frac{?}{2}$

Formulate an LP that can be used to minimize the fuel cost incurred in completing the schedule.

Note: You only need to formulate the problem, no need to solve it$.$

Question $2(6$pts$)$: Consider the following LP:

Maxz$=x_1+x_2$