Hello,Originally Posted byChrissy

let x be the times which the price is increased. Then you get:

new price: 10 + .5*x

number of sold cakes: 200 - 5*x

money to be paid for the cakes: (200-5*x)*6

profit with respect to x : p(x)

Now you can form an equation

p(x) = (200-5*x)*(10+.5*x)-(200-5*x)*6

1. The graph of this function is a parabola where the vertex is at the maximum value. If you tranform this equation into the vertex form (?) of the parabola you'll get:

. That means: If the price is increased 16 times by 0.5 $ then the profit will be 1440$ instead of the initial 800 $.

2. You'll get the maximum of p if the 1rst derivative equals zero:

. Let the RHS be zero, then x = 16. Plug in this value for x into p(x) and you'll get 1440 $.

Bon appetit!

EB