A store has been selling 100 Blu-ray disc players a week at $600 each. A market survey indicates that for each $40 rebate offered to buyers, the number of units sold will increase by 80 a week. Find the demand function and the revenue function. How large a rebate should the store offer to maximize its revenue

The rebate should be $220

Step-by-step explanation:

Demand Curve

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

step-by-step explanation: a reaction is first order. if the initial reactant concentration is 0.0200 m, and 25.0 days later the concentration is 6.25 x 10-4 m, then its half-life is:

i don't even know how to read that, ill try to do it if you translate it into english.