.
The total length of the parade is the number of large floats times 40' plus the number of small floats times 25'.
Large Small Length Cost 0 8 200 2400 Too long 0 7 175 2100 Possible 0 6 150 1800 Possible 0 5 125 1500 Too Short 1 7 215 2700 Too Long, Over Budget 1 6 190 2400 Possible 1 5 165 2100 Possible 1 4 140 1800 Too Short 2 5 205 2700 Too Long, Over Budget 2 4 180 2400 Possible 2 3 155 2100 Possible 2 2 130 1800 Too Short 3 4 220 3000 Too Long, Over Budget 3 3 195 2700 Over Budget 3 2 170 2400 Possible 3 1 145 2100 Too Short 4 2 210 3000 Too Long, Over Budget 4 1 185 2700 Over Budget 4 0 160 2400 Possible 5 0 200 3000 Too Long, Over Budget
Note that zero large and eight small is an invalid combination because that would be exactly 200 feet and 200 feet is NOT less than 200 feet. Furthermore, you cannot discount the 10 feet required behind each float even for the last float since the problem doesn't say "10 feet will be left after each float except for the last float" Five large and zero small is invalid for the same reasons.
Zero large and six small IS a valid combination because 150 IS at least 150.
John
My calculator said it, I believe it, that settles it
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