math help

Lyle is replacing light bulbs in his apartment.
He is using energy-saving bulbs and regular bulbs, and wants to use 21 or fewer bulbs
altogether.
He wants no more than 18 energy-saving bulbs and at least 2 regular bulbs.
The energy-saving bulbs cost $5.95 each, and the regular bulbs cost $7.85 each.
What is the most Lyle can spend on replacement bulbs? How many of each will be use?

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  1. s </= 18
    r >/= 2
    cost = 5.95 s + 7.85 r
    s + r </= 21
    maximize cost (for some reason) (so use all expensive ones but not to jump to conclusion)
    graph it, I did s hor (x axis) and r vertical (y axis)
    below line sloping down from (0,21) to ( 21,0) which is is r =21 - s
    left of (18,0)
    above r = 2
    useful intersections are (0,21) and the intersection of s = 18 and r = 21-s
    which is (18,3)
    calculate
    cost = 5.95 s + 7.85 r
    at those two points and pick the higher one (obviously regular = 21)
    I suspect a typo but gave you the method anyway.

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