Answer:
<em>The rebate should be $220</em>
Step-by-step explanation:
<u>Demand Curve</u>
It's the relationship between price (P) and quantity (Q) demanded a certain product or service.
(a) We need to find the function that relates both magnitudes assuming a linear equation. The equation of a line can be found with the point-point formula:
Two sets of data are given: 100 Blu-ray disc players are sold a week at $600 each. The ordered pair for this condition is (P,Q)=(600,100).
The other point comes from the market survey: The number of units sold will increase by 80 (100+80=180) when the price goes down $40 (600-40=560). The new point is (P,Q)=(560,180)
We set up the equation of the demand
Rearranging
Or
Simplifying
(b) The revenue function is Q times the price
Solving the equation of the demand for P
Thus, the revenue is
(c) To find the optimum value of the revenue, we take the derivative of R and equate to 0
Solving
Q=560 units a week
For which the revenue is
And the price is
The rebate should be $600-$280=$220