Ok i thought i could help but the most i could do with the 12x and 28y was do then by them self to get 84 i will keep trying though ok?
It is convenient to let a spreadsheet or graphing calculator do the math for this. Functions can be defined for cost and profit, and evaluated at each of the volumes of interest.
a1) For 200 cars, the Outside location yields the greatest profit
a2) For 300 cars, the City location yields the greatest profit
b) The sites yield the same profit for a volume of 278 cars.
General rule for the reflection. r(x,y,z)= f(x,-y,z)
Results:
P: (0, - 5, 4)
Y: (-2, - 7, 4)
R: (0, - 7, 4)
A: (0, - 7, 6)
General rule for the translation: t(x,y,z) = r(x+2, y-4,z+3)
Result:
P: (0-2, -5+4 , 4-3) = (-2, -1, 1)
Y: (-2-2, - 7+4, 4-3) = (-4, -3, 1)
R: (0-2, - 7+4, 4-3) = (-2, -3, 1)
A: (0-2, - 7+4, 6-3) = (-2, -3, 3)