SOLUTION: The Diver Time company makes digital watches for scuba divers. The company models its profits with the function P(d) = −2d2+13d−6, where d is the number of watches sold, in hu

You are given a quadratic function  

    P(d) = -2d^2 + 13d - 6.    (1)


The function gas a negative leading coefficient -2 at the quadratic term d^2,  therefore, the function is a parabola

turned down.  It is very well known fact that such a quadratic function gets its maximum at the point

    d = ,

where "a" is the coefficient at the squared term and "b" is the coefficient at the linear term.


In your case  a= -2,  b= 13,  therefore the quadratic function gets its maximum value at

     =  =  = 3.25


It means that the company should sell    hundreds of watches, or  325 watches.


Part (a) is completed and the answer is  3.25 hundreds of watches should be sold (or 325 watches).

To find the maximum profit, substitute the found value of   = 3.25  into the formula (1)  to get


     = P(3.25) = -2*3.25^2 + 13*3.25 + 6 = 27.125  tens thousands of dollars, or $271,250.