Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / The average cost function for the weekly manufacture of portable CD players is given by C(x)=140,000x−1+20+0
The average cost function for the weekly manufacture of portable CD players is given by C(x)=140,000x−1+20+0.0002xC(x)=140,000x−1+20+0.0002x dollars per player, where xx is the number of CD players manufactured that week. Weekly production is currently 2,0002,000 players and is increasing at a rate of 100100 players per week. At what rate the average is the average cost changing when current production is 20002000 players per week?
From the given information, the cost function is
C(x)=140000x−1+20+0.0002xC(x)=140000x−1+20+0.0002x dollars per year.
And the production for current week is, x=2000x=2000 players.
And the given increasing rate of change for production with respect to t,t, is dxdt=100dxdt=100 players per week. Where tt is time.
Now, the rate of change for average cost is,
dCdt=dCdx⋅dxdt.dCdt=dCdx⋅dxdt.
dCdt=ddx(140000x−1+20+0.0002x)⋅dxdt=ddx(140000x−1⋅dxdt+20⋅dxdt+0.0002x⋅dxdt)=[ddx(140000x)⋅dxdt−ddx(1)⋅dxdt+ddx(20)⋅dxdt+ddx(0.0002x))⋅dxdt]=[140000ddx(x)⋅dxdt−0⋅dxdt+0⋅dxdt+0.0002ddx(x)⋅dxdt]=[140000⋅dxdt−0+0+0.0002⋅dxdt]=[140000(100)+0.0002(100)](?dxdt=100)=[14000000+0.02]dCdt=14000000.02.dCdt=ddx(140000x−1+20+0.0002x)⋅dxdt=ddx(140000x−1⋅dxdt+20⋅dxdt+0.0002x⋅dxdt)=[ddx(140000x)⋅dxdt−ddx(1)⋅dxdt+ddx(20)⋅dxdt+ddx(0.0002x))⋅dxdt]=[140000ddx(x)⋅dxdt−0⋅dxdt+0⋅dxdt+0.0002ddx(x)⋅dxdt]=[140000⋅dxdt−0+0+0.0002⋅dxdt]=[140000(100)+0.0002(100)](?dxdt=100)=[14000000+0.02]dCdt=14000000.02.
Let's consider the given cost function as, C(x),C(x), where xx is the number of CD players manufactured per week. Now we need to find the rate of change of average cost, which is, dCdt.dCdt.
To find that, the formula is,
dCdt=dCdx⋅dxdt.dCdt=dCdx⋅dxdt. Therefore, we need to find the answer, by using the differential method.
