This is a beam supported at both ends with a single center load. The most concern in this appliaction is the compressive stress along the beam span.
The section of a 2x4 lumber is 3.5" x 1.5", beam length 10 FT,
Maxium compress stength of grade 2 white pine is 4800 psi, from my calculation, allowed max load at the beam center is about 490 lbs. With double 2x4 lumber, the max allowed load is 980 lbs.
Take safe factor as 3, max load for this design should be 330 lbs. Under such load, the sag at the center is about 0.9 inch.
Shear stress under 330 lbs is 63psi, which is far below the max shear strength 900 psi.
In conclution, I would appove this design if I have a stamp.