Question

Let the price and quantity functions of a product be given by p = 2x + k and q = x + 2 respectively, where x is a variable and k is a constant. Find the value(s) of k for which the total revenue function is always positive.

Answer 1

Maybe the values of k is whole numbers

Step by step process:

the price function of a product be given by p = 2x + k

the quantity function of a product be given by q = x + 2

where x is a variable and k is a constant.

Then the total revenue function(T) = p × q

= (2x + k)(x + 2)

= 2x^2 + 4x+ kx +2k

= 2x^2 + (4+k) x + 2k

There the values of k is whole numbers.