Oh boy I can do this problem! =D
y = x2 + 8x - 9
We need to take the derivative of this. That will tell us the slope of the graph of this function at any point. Take the derivative using the power rule.
y' = 2x + 8
Set y' = 0 to find all the places where the slope of x2 + 8x - 9 is zero.
0 = 2x + 8
-8 = 2x
-4 = x
So when x is -4, the slope of x2 + 8x - 9 is zero. That means it is either a maximum, minimum, or inflection point. To figure out which one, take the second derivative.
Since y'' is positive when x is -4, that means the graph is concave up, which means x = -4 is the minimum.
7500/3 = 2500
So 2500 of the shippings are peanut free.
7500 - 2500 = 5000
So 5000 of the shippings are mints/store brand.
If I understand your question correctly, you are saying that the company makes money on 60% of peanut free chocolates and 50% of mint/store brand chocolates. But we want to know how much the store makes, not the company. That means the store makes money on the remaining 40% of peanut free chocolates and the remaining 50% of mint/store brand chocolates.
40% of 2500 = (0.4)(2500) = 1000
50% of 5000 = (0.5)(5000) = 2500
1000 + 2500 = 3500
So the store makes money on 3500 shippings every day.