Answer:
4 units per week
Explanation:
Calculation to Find the rate of change of sales
First step
dP/dt=5600
Second step
Since the revenue is the product of demand and sales
Hence,
R(x)=px
=(6000-25x)x
=6000x-25x²
Third step is to determine the profit which is the difference of revenue and cost.
Hence,
P(x)=R(x)-C(x)
=6000x-25x²-(2400x+ 5200)
=6000x- 25x² -2400x-5200
=3600x-25x²-5200
Fourth step is to Differentiate the profit with respect to time
dP/dt=3600 dx/dt- 50 dx/dt-0
=50(3600/50-x) dx/dt
=50(72-x) dx/dt
Now let Find the rate of change of sales when dP/dt=5600 and x =44
5600=50(72-44) dx/dt
5600=50(28) dx/dt
5600=1400 dx/dt
dx/dt=5600/1400
dx/dt= 4 units per week
Therefore the rate of change of sales is 4 units per week
