On every vehicle sold in the US, there is a sticker – commonly called the tire placard - that lists the original tire size and the proper pressure for that size. The placard is usually located on a doorpost or in the glove box – but sometimes it is located in the trunk or on the fuel filler door.
If you have a different tire size than is listed on the placard, then the pressure should be recalculated based on the original load carrying capacity as expressed by the placard tire size and pressure. The calculation isn't difficult, but it requires the use of tire load tables - which are not allowed to be published on the 'net.
But I happen to have a copy and can do the calculation for you, but I am going to need 3 tidbits of information
1) The placard tire size
2) The placard tire pressure
3) The new tire size.
Well ....... we have all 3! Cool!!
So a P235/75R15 XL inflated to 40 psi front and 45 psi rear .....
OK, first problem. I know this is wrong. An Extra Load tire would not be specified at 45 psi by Ford. And when I look up Ford pickups in Tire Guides, it tells me that 15" tires haven't been supplied to F-150's since 1996, and they list ALL Ford pickups with this tire as using 35 psi front and 41 psi rear. While I'm not 100% convinced this is true, it isn't unreasonable, so I'm going to use those values.
Oilboy - Look for the placard (Should be on the driver's doorpost down near the door sill) and see if that information is correct. If it isn't, then the rest of this is also incorrect.
To get the same load carrying capacity, then a 31X10.50R15LT needs to use: 37 psi front / 41 psi rear