A medical supply company has 1150 worker-hours for production, maintenance, and inspection. Using this and other factors, the number of hours used for each operation, P, M, and I, respectively, is found by solving the following system of equations. Find P, M and I.
P + M + I = 1150
P = 4I - 100
P = 6M + 50
equate the right sides of the last two, since both equal to P
4l - 100 = 6M + 50
4l - 6M = 150 --> l = (150+6M)/4
into the first:
P + M + I = 1150
(6M+50) + M + (150+6M)/4 = 1150
24M + 200 + 4M + 150 + 6M = 4600
34M = 4250
M = 125
so P = 6(125) + 50 = 800
l = (150 + 750)/4 = 225
P=800 , M=125, l = 225