A garden supply company wants to maximize weekly profit P = 40x + 55y, where x is bags of standard mix and y is bags of premium mix produced, subject to 2x + 3y ≤ 1200 (mixing-machine hours) and x + 2y ≤ 700 (bagging-line hours), with x ≥ 0 and y ≥ 0. The graph below shows the two boundary lines of the feasible region. What is the maximum possible weekly profit?
A$23,000, produced as 300 bags of standard mix and 200 bags of premium mix
B$24,000, produced as 600 bags of standard mix and 0 bags of premium mix
C$19,250, produced as 0 bags of standard mix and 350 bags of premium mix
D$28,000, produced as 700 bags of standard mix and 0 bags of premium mix
Explanation
The feasible region's corner points are (0,0), (600,0) [from 2x+3y=1200 at y=0, since that is the binding constraint there], (300,200) [intersection of the two lines], and (0,350) [from x+2y=700 at x=0, the binding constraint there]. Evaluating P=40x+55y: (0,0)→0; (600,0)→24000; (300,200)→23000; (0,350)→19250. The maximum is $24,000 at (600,0). Note (700,0) is NOT feasible — it violates 2x+3y≤1200 since 2(700)=1400>1200.
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