A front of a building 50 m by 16 m is to be illuminated by sixteen 1000-W lamps arranged so that uniform illumination is obtained at the surface. Assuming a luminous efficiency of 18 lumens/watt, CU = 0.50 and MF = 0.90, what is the illumination on the surface?

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Hello, I am doing some practice and I am getting hung up on my cross product derivation. I know it is supposed to be zero, but I want to prove it with the math. Could you help me out with this? Thank you for your time and effort, I appreciate the help.  Please see attached for probelm.

Refer to the National Electrical Code® or the working drawings when necessary. Where applicable, responses should be written in complete sentences. For problems 1 and 2, six luminaires, similar to Style E used in the Commercial Building, are to be installed in a room that is 12 ft x 18 ft (~3.7 m x ~5.5 m) with a 9 ft (2.8 m) floor-to-ceiling height. The spacing ratio for the luminaire is 1:0. 1. The maximum distance that the luminaires can be separated and achieve uniform illuminance is ft ( m). For problems 2-5, two luminaires, 8 ft (2.5 m) and 4 ft (1.2 m) in length with dimensions as shown in Figure 15-7, are to be installed in tandem (end to end). The end of the long luminaire is to be 2 ft (600 mm) from the wall. 2. The center of the outlet box should be roughed in at ft ( m) from the wall. 3. The first support should be installed at the wall. ft ( m) from 4. The second support should be installed at from the wall. ft ( m) 5. The final support should be installed at the wall. ft…