# 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...

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`