you want to maximize p = 190x+220y subject to the constraints
x>=0
y>=0
5x+6y <= 60
so evaluate p at (0,10), (12,0) to find the maximum
A chain saw requires 5 hours of assembly and a wood chipper 6 hours a maximum of 60 hours of assembly time is available the profit is $190 on a chain saw and $220 on a chipper how many of each should be assembled for maximum profit
2 answers
p = 190 s + 220 c
60 >/= 5 s + 6 c
s on x axis , c on y axis
5 s + 6 c </= 60 is left of line from point A = (0,10) down to Point B (12,0)
check p along that line { c = 10 - (10/12) s }
at A
p = 190 *0 + 220 * 10 = 2200
at B
p =190 *12 + 220 *0 = 2280
try elsewhere on the line, for example ( 6, 5)
p = 190 * 6 + 220 * 5 = 1140 + 1100= 2240 at point B
in fact I doubt you will find any point on that line with profit more than2280
at Point B
60 >/= 5 s + 6 c
s on x axis , c on y axis
5 s + 6 c </= 60 is left of line from point A = (0,10) down to Point B (12,0)
check p along that line { c = 10 - (10/12) s }
at A
p = 190 *0 + 220 * 10 = 2200
at B
p =190 *12 + 220 *0 = 2280
try elsewhere on the line, for example ( 6, 5)
p = 190 * 6 + 220 * 5 = 1140 + 1100= 2240 at point B
in fact I doubt you will find any point on that line with profit more than2280
at Point B