Answer:
The answer is "70 units".
Explanation:
In the given question some equation is missing which can be defined as follows:
[tex]C = 1.5Q^2+40Q\\\\P=320-0.5Q[/tex]
Monopolistic functions are used where Marginal Profit = Marginal Cost where marginal revenue and marginal cost stand for the MR and MC.
Finding the value of MR :
[tex]\ MR = \frac{\partial TR}{\partial Q} \\\\[/tex]
[tex]= \frac{\partial PQ}{\partial Q} \\\\= \frac{\partial (320-0.5Q)Q}{\partial Q}[/tex]
[tex]= \frac{\partial (320Q -0.5Q^2)}{\partial Q}\\\\ = \frac{\partial Q (320 -0.5Q)}{\partial Q}\\\\ \ by \ solving \ we \ get \\\\ = 320 - Q...(1)[/tex]
Calculating the value of the MC:
[tex]MC = \frac{\partial TC}{\partial Q} \\[/tex]
[tex]=\frac{\partial (1.5Q^2 + 40Q)}{\partial Q} \\\\=\frac{\partial Q (1.5Q + 40)}{\partial Q}\\\\ \ by \ solve \ value \\\\ = 3Q + 40....(2)[/tex]
compare the above equation (i) and (ii):
[tex]\to 320 -Q = 3Q+40\\\\\to 320 -40 = 3Q+ Q\\\\\to 280 = 4Q\\\\\to 4Q =280 \\\\\to Q= \frac{280}{4}\\\\\to Q= 70 \\[/tex]
