$4.[5$ points$]$

$($b$),($c$)$ and $($d$)$ using sensitivity analysis.

Subject to:

$=20001+30002+50003+40004$

$1001+1002+1003+1004<=4000101+102+203+204<=600201+202+303+204<=900201+102+303+304<=700$

$1,2,3,4>=0$

Solve the following linear program. You can use a solver. Explain your answers to parts

a$.$ What is the optimal solution?

b$.$ For what range in variations in $3=5000$ from the optimization function does

the current basis remain optimal?

c$.$ If the first constraint $1=4000$ changes, for what range of supply will the basis

remain optimal?

d$.$ If the supply is within the range given by part $($b$),$ what will the profit be$?$