Step-by-step explanation:
Since we are not given the cost function, let the cost function be expressed as C(x) = 0.2x²-2.6x+9.950
where C(x) is in hundreds of dollars.
x is the number of bicycle built
In order to minimize the average cost of the bicycle, then d(C(x))/dx = 0
d(C(x))/dx = 2(0.2)x²⁻¹ - 2.6
d(C(x))/dx = 2(0.2)x- 2.6
d(C(x))/dx = 0.4x- 2.6
Since d(C(x))/dx =0, then;
0.4x - 2.6 = 0
0.4x = 2.6
x = 2.6/0.4
x = 6.5
Hence around 6 bicycles should be built by the shop to minimize the average cost per bicycle
The number of bicycles should the shop build to minimize the average cost per bicycle should be 6.
For minimize the average cost of the bicycle,
So [tex]d(C(x))\div dx = 0[/tex]
Now
[tex]d(C(x))\div dx = 2(0.2)x^{2-1} - 2.6\\\\d(C(x))\div dx = 2(0.2)x- 2.6\\\\d(C(x))\div dx = 0.4x- 2.6\\\\0.4x - 2.6 = 0\\\\0.4x = 2.6\\\\x = 2.6\div 0.4[/tex]
x = 6.5
This is an incomplete question. Here is the missing details:
The cost function be expressed as C(x) = 0.2x²-2.6x+9.950
where C(x) is in hundreds of dollars.
x is the number of bicycle built
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