Per tech sheet 7040 has a weak 180w psu.  you might add a low profile low power entry level gpu to it such as gt730, gt1030, gt710, but even these would push psu to the limit.  What is your gpu upgrade purpose?  Is it for gaming or just higher resolution?

basic online calculator estimates psu assuming i7-6700,16Gb ddr4,sata ssd,dvd,gt 710

Load Wattage: 182 W
Recommended PSU Wattage: 232 W

if you add gt730 or gr1030, psu is too weak (unless you disconnect power to dvd)

you may be able to upgrade psu to a higher power, but out of the box you get only 180w.  The psu uses proprietary 8 pin ATX and is TFX form factor.

you can glance at the tech sheet to get a quick summary of 7040 spec.

Thanks for the tips!

Yes, I was looking into building a budget gaming pc. It doesn’t have to be anything crazy but it wouldn’t take much to best my 2015 Dell Inspiron 15r5537 with an old i5 and Intel hd family integrated gpu  

Good thinking on the psu. That honestly didn’t even cross my mind...not sure why.

I’ve never built a pc and figured I’d ask around if it was worth it even possible to upgrade a pc like the 7040 vs dropping $1300+ on a custom built entry level gaming pc. 

Re: upgrade a pc like the 7040 vs dropping $1300+ on a custom built entry level gaming pc. 

if it is not using the latest graphics card, build your own custom pc is less expensive.

since you have never built one, do not start with SFF which has too many limitations for beginner builder.  start from mini tower optiplex is easier.

Just FYI, the GT 730 does not fit - it hits the power supply. Is there another one you can suggest? Please edit / update post for accuracy.

7040SFF motherboard has its PCIex16 slot right next to psu.  Only single slot width low profile card with low profile heatsink may fit.  Some single slot width gpu including gt730 has a somewhat bulky heatsink that can bang into the psu when I stalked into x16 slot.  If the GT730 in x16 slot is hitting psu, I suggest install GT730 in the PCIex4 slot so it would not hit the psu.  The x4 slot has an open end and accommodates x16 card.  The speed sacrifice is minimal.

I saw this recently

https://youtu.be/CTI9-BCauX8

Optiplex 7040 SFF has a 180 w PSU.

You will need a GT 1030 as your best option.

GT 1030 is good for video editing and moderate gaming, it consumes 30 W maximum. It doesn't need a power connecter from the PSU. 

P.S: if you have a 240 W PSU you can have a GTX 1650 instead.

@redxps630​ 7040's only eats 93 watts max (people have done tests on this) the extra gpu runs at 55 watts so in the worst case which should only happen when restarting you should only use 148 watts max considering that the psu is 80 bronze aka 85% efficiency 180 divided by 100 x 85 = 153 so in the worst case you should be using 148/153 watts being used isn't ideal but should still work