Better Students Ask More Questions.
The price of a product varies with the quantity bought as P(x) = 360 - 12*x^2 + 3x. How...
1 Answer | add yours
From the information provided in the problem, the price of x units of the product is given by P(x) = 360 - 12x^2 + 3x. The price unit for x products bought is Pp(x) = 360/x - 12x + 3. The number of units to be bought to minimize the price per unit could be calculate by solving Pp'(x) = 0 for x but it should be kept in mind that the price cannot be negative. The graph of Pp(x) is shown below.
Solving 360/x - 12x + 3 = 0
=> 360 - 12x^2 + 3x = 0
The quadratic equation has a positive root of `(sqrt(1921)+1)/8 ~~ 5.6` , this can be rounded to 6.
To minimize the price per unit one would have to buy 6 units of the product.
Posted by justaguide on March 17, 2013 at 5:29 AM (Answer #1)
Join to answer this question
Join a community of thousands of dedicated teachers and students.