SOLUTION: A fruit juice company varies the price of its litre cartons to maximise profit. The equation that models the company's profit is given below:
P=-80d^2+960d-2280
Where P is the pr
Algebra ->
Quadratic Equations and Parabolas
-> SOLUTION: A fruit juice company varies the price of its litre cartons to maximise profit. The equation that models the company's profit is given below:
P=-80d^2+960d-2280
Where P is the pr
Log On
Question 1144637: A fruit juice company varies the price of its litre cartons to maximise profit. The equation that models the company's profit is given below:
P=-80d^2+960d-2280
Where P is the profit in thousands of dollars and d is the price of a litre carton in dollars.
a) What is the maximum profit the company can make selling litre containers?
b) Sketch the general shape of the graph showing how profit varies with the price of a litre container.
c) What's the lowest price the company can sell litre cartons for and still break even? (Answer to the nearest 10 cents) Answer by ikleyn(52779) (Show Source):
(a) Function P(d) = - 80d^2 + 960d - 2280 is a quadratic function of the argument (variable) "d".
For any quadratic function f(x) = ax^2 + bx + c with negative leading coefficient "a" at x^2,
its maximum is achieved at the value of = .
In your case, a= -80, b= 960. Therefore
= = = 6.
Thus the optimum price is 6 dollars (or whatever monetary units) per cartoon.
It provides the maximum profit of P(6) = -80*6^2 + 960*6 -2280 = 600 thousands of your monetary units.
(b) Make a plot on your own. // When a "student" asks me to make a plot, I always think that it is his (or her) job - not my.
(c) To answer this question, solve this quadratic equation
P(d) = 0, or -80*d^2 + 960*d -2280 = 0.
