Answer:
Increasing by $66 per day
Step-by-step explanation:
If sales are dropping at a rate of 2 per day, the sales function is:
[tex]S = -2t +80[/tex]
If price is increasing by $1 per day, the daily price function is:
[tex]P=1t+7[/tex]
Revenue is given by daily sales multiplied by daily price:
[tex]R = S(t)*P(t) = (-2t+80)*(t+7)\\R(t) = -2t^2+66t+560[/tex]
The derivate of the revenue function gives us the daily rate of change in revenue:
[tex]R(t) = -2t^2+66t+560\\R'(t) = -4t+66[/tex]
Currently (t=0) her daily revenue is changing by:
[tex]R'(0) = -4*0+66\\R'(0) = \$66[/tex]
Her revenue is increasing by $66 per day.
The revenue should be increased by $66 per day.
In the case when sales are dropping at a rate of 2 per day, the sales function is:
S = -2t + 80
Now
In the case when the price is increasing by $1 per day, the daily price function is:
P = 1t + 7
Now the revenue should be
[tex]= -2t + 80 \times 1t + 7\\\\= -2t^2 + 66t + 560\\\\= -4t + 66[/tex]
Now
= -4(0) + 66
= -0 + 66
= $66
Learn more about the revenue here: https://brainly.com/question/24610608
