Chapter 3.4, Problem 31AYU

To determine

To find: how the revenue is $0 when the price charged is $140

Answer to Problem 31AYU

The total revenue gained would be again $0

Explanation of Solution

Given:

If the price charged for the calculators is $0 or $140 the revenue is $0.

Calculation:

In Texas instruments, the marketing department sold calculators at a price of $p$ dollars perunit, the number $x$ of calculators sold is given by the demand equation

  $x=21000-150p$

And total revenue gained is given by the relation

  $R=xp=(21000-150p)p=-150p^2+21000p$

Now it is clear that if the price charged for calculator is $p=\$0$ , the revenue is $R=\$0$ .

Further on plug in $p=140$ in the equation of revenue function,

  $R(140)=-150{(140)}^2+21000\times 140=-150\times 19600+2940000=-2940000+2940000$

  $=0$

By the above calculation, it is clear that if the price of each calculator is fixed for $140, the total revenue gained be would again $0.

Conclusion:

Therefore, the total revenue gained would be again $0 .