Question

the daily profit p for a cake bakery can be modeled by the function
`p(x) = - 13x {}^(2) + 280x - 711`where x is the price of a cake. what should the price of a cake be to provide a daily profit of at least $600? round your answer(s) tot he nearest doller.

Answer 1

Profit expressed by means of a quadratic equation

Then Profit daily basis is equal to

-13x^2 + 280 x - 711

must be equal to 600

Then write

-13 x^2 + 280x -711= 600

rewrite and solve for x

-13 x^2 + 280x - 1311 = 0

x^ 2 - (280/13)x +(1311/13) = 0

It gives 2 solutions, one positive, another negative. But we are only interested in positive solutions.

then find 2 numbers m,n such that

m•n = (1311//13)

And

m+n = (-280/13)

m-n = √ (280/13)^2 - 4 (1311/13)

m- n = [√ (280^2 - 4•1311•13) ]/ 13

m-n = 101.13/13 = 7.78

Now

x = - b/2 ± 7.78/2