Question

Please show steps!!!

Answer 1

Answer:

  there is no price for which weekly revenue would be 1800

Step-by-step explanation:

If there is a solution to the equation ...

  r = 1800 = -4p² +40p +1287

then there is a solution to ...

  4p² -40p +513 = 0

Comparing this to the standard form quadratic equation

  $ax^2+bx+c=0$

we can match coefficients to see that ...

• a = 4
• b = -40
• c = 513

The discriminant of a quadratic is ...

  $d=b^2-4ac\\\\d=(-40)^2-4(4)(513) = 1600-8208 = -6608$

When we fill in the numbers and evaluate, we find the discriminant is negative. This tells us that solutions to the equation are complex—there are no real solutions, meaning there is no price that will give $1800 weekly revenue.

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A graph shows the highest weekly revenue obtainable at any price is $1387, so there is no price that will give revenue of $1800.