a producer find that demand for his commodity obeys a linear equation p+0.45x=6, where p is in dollars and x in thousands of units.
Find the level of production that will maximize the revenue
the level of production is=
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We can solve for "p" to know the function for price.
So, we subtract both sides by 0.45x.
`p + 0.45x - 0.45x = 6 - 0.45x`
`p = -0.45x + 6`
We know that revenue = price * amount of units sold.
So, we will have:
`r = (-0.45x + 6)(x) `
Use Distributive property.
`r = -0.45x^2 + 6x`
Take the derivative of both sides.
`r' = -0.9x + 6`
Equate it to zero.
`-0.9x + 6 = 0`
Subtract both sides by 6.
`-0.9x = -6`
Divide both sides by -0.9.
`x = 6.67 or 7.0`
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