Find Optimal t for Profit: C vs. R

[alllove]

The cost of producing t units is C = 3t2 + 9t, and the revenue generated from sales is R = 4t2 + t. Determine the number of units to be sold in order to generate a profit.

Select one:
A. t > 8
B. t > 10
C. t > 9
D. t > 0

 

[kaliprasad]

For the profit we must have $R > C$

or $4t^2+t > 3t^2 + 9t$

Now you can proceed from here and find the result

 

[HOI]

Another way of looking at it: "profit" is "revenue minus costs", R- C= 4t^2+ t- (3t^2+ 9t)= t^2- 8t. The "break even" point, separating "loss" and "profit" is where that is 0. Solve t^2- 8t= 0.

(Using "^" to indicate powers makes it easier to read: "t^2" rather than "t2".)