Minima Maxim/ax+by=c table
why is the maximum at x=167 and y=29
Since 16y+15x needs to be maximised i thought x and y should be as close as possible with y greater than x since y's coefficient is greater
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Your reasoning assumes that since the coefficient of y (16) is larger than the coefficient of x (15), increasing y should increase the total males. But x and y are not independent. They are tied by the constraint 29x + 33y = 5800. When y increases by 1, x must decrease by about 33/29 ≈ 1.14 to keep the total fixed. This drop in x reduces the male count more than the small gain from increasing y. So the expression 15x + 16y actually decreases as y increases, meaning the maximum occurs when y is as small as possible.
Okay thank you!