Grush Consulting has five projects to consider. Each will require time in the next two quarters according to the table below.

Project

Time in First Quarter

Time in Second Quarter

Revenue

A

$5$

$8$

$12,000$

B

$3$

$12$

$10,000$

C

$7$

$5$

$15,000$

D

$2$

$3$

$5,000$

E

$15$

$1$

$20,000$

$$

Revenue from each project is also shown. Develop a model whose solution would maximize revenue, meet the time budget of $25$ in the first quarter and $20$ in the second quarter, and not do both projects C and D$.$

Let A $=1$ if project A is selected, $0$ otherwise; same for B$,$ C$,$ D$,$ and E

Group of answer choices

Max $12,000$A $+10,000$B $+15,000$C $+5,000$D $+20,000$E

s$.$t$.5$A $+3$B $+7$C $+2$D $+15$E $<=25$

$8$A $+12$B $+5$C $+3$D $+1$E $<=20$

C $+$ D $<=1$

Min $12,000$A $+10,000$B $+15,000$C $+5,000$D $+20,000$E

s$.$t$.5$A $+3$B $+7$C $+2$D $+15$E $>=25$

$8$A $+12$B $+5$C $+3$D $+1$E $>=20$

C $+$ D $>=1$

Max A $+$ B $+$ C $+$ D $+$ E

s$.$t$.5$A $+8$B $<=12,000$

$3$B $+12$C $<=10,000$

$7$C $+5$D $<=15,000$

$2$D $+3$E $<=5,000$

$15$E $<=20,000$

Max $12,000$A $+10,000$B $+15,000$C $+5,000$D $+20,000$E

s$.$t$.13$A $+15$B $+12$C $+5$D $+16$E $<=45$

C $+$ D $>=1$