Answer:
(a) 3, (b) 96, (c) No
Step-by-step explanation:
(a) Since we have [tex]p = 150 - 6q^2[/tex] and [tex]p = 10q^2 + 2q[/tex], we can set up a quadratic equation by [tex]150 - 6q^2 = 10q^2 + 2q[/tex], moving all values to one side.
The equation is: [tex]16q^2 + 2q - 150 = 0[/tex].
Let's use the quadratic formula to find q,
we obtain that [tex]q = 3[/tex] or [tex]q = -3.125[/tex]
We can ignore [tex]-3.125[/tex] because supplying a negative quantity is impossible.
Hence, the answer of (a) is 3
(b) Simply substitute [tex]q = 3[/tex] into either equations given in the question to find p, and the answer of (b) is 96.
(c) We want to find if there is an exact quantity that makes the TR exactly 1500.
We substitute TR = 1500,
[tex]1500 = 85q - 2q^2[/tex]
Use the quadratic formula again, and we will find that the answer is "undefined".
As a result, there is not output level in which the total revenue is exactly 1500.
