With a markup of x%, the number of customers is given by:
With each customer buying an average of ŁA in goods per week, the weekly revenue in pounds is then:
The weekly profit is then:
In order to find the markup which yields the maximum profit, I would write the profit function as:
Now, either equate the first derivative to zero to find the critical markup, or find the axis of symmetry for the parabolic profit function.