What you posted here will be happy to accept the profit formula P = R -C.
I always say that in solving word problems, if you know what the problem is asking you to find then you solved 30% of the problem already. (No relation to your problem here also? )
Anyway, so the problem is asking you about profits. How many pounds of choc creams to sell for maximum profit. Find the value of x then that will give maximum profit. (Understanding the what-is-to-find is more confusing than the problem. . Not really. It only seems that way.)
Okay, find x that maximizes the profit.
Profit = Revenue minus Cost
P = 11x -(0.01x^2 +625)
P = 11x -0.01x^2 -625 ---------------(i)
If you know Calculus, you can get the derivative of P with respect to x, set that to zero, then you'd get the answer. Check only if the x you'd get maximizes the P. It could minimize the P for all we know.
If you are not into Calculus yet, use Analytic Geometry, or the property of a vertical parabola. Find the vertex of the P parabola. If it is the highest point, you got it. If it is the lowest point, review your solution, something is wrong.
Say you know about derivatives. Differentiate (i) with respect to x,
dP/dx = 11 -0.02x
Set that to zero,
0.02x = 11
x = 11 /0.02 = 550 lbs. choc creams
Is that for maximum?
Get the 2nd derivative of P.
P'' = -0.02 -----always negative, the concavity of the curve is facing downward, so 550 is for maximum.
Therefore, Sweet shop company will maximize its profits if it sells 550 pounds of chocolate creams. -----------answer.