The revenue from the sale of a product is given by R=1642x-11x^2 - x^3.?

 If the sale of 11 units gives a total revenue of 15400$, find another number of units that will give 15400$ in revenue.

4 Answers

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  • 1 month ago

    You are given:

    R = 1642x - 11x² - x³

    We are interested in values that make R = 15400, so let's set that in place and put it into standard form:

    15400 = 1642x - 11x² - x³

    0 = 1642x - 11x² - x³ - 15400

    0 = -x³ - 11x² + 1642x - 15400

    Let's multiply both sides by -1 to simplify as I don't like having a negative leading coefficient if I can help it:

    0 = x³ + 11x² - 1642x + 15400

    We are told that x = 11 is a solution to this quadratic so (x - 11) must be a factor. We can divide the cubic by the linear expression to get a quadratic in result:

    . . . . .__x²_+_22x_-_1400__________

    x - 11 ) x³ + 11x² - 1642x + 15400

    . . . . . .x³ - 11x²

    . . . . . ---------------

    . . . . . . . . . 22x² - 1642x + 15400

    . . . . . . . . . 22x² - 242x

    . . . . . . . . ------------------------

    . . . . . . . . . . . . . -1400x + 15400

    . . . . . . . . . . . . . -1400x + 15400

    . . . . . . . . . . . . .-------------------------

    . . . . . . . . . . . . . . . . . . . . . . . 0

    Now we have this quadratic to be solved:

    x² + 22x - 1400 = 0

    x = [ -b ± √(b² - 4ac)] / (2a)

    x = [ -22 ± √(22² - 4(1)(-1400))] / (2 * 1)

    x = [ -22 ± √(484 + 5600)] / 2

    x = [ -22 ± √(6084)] / 2

    x = (-22 ± 78) / 2

    x = -100/2 and 56/2

    x = -50 and 28

    We aren't interested in the negative value, so the other solution that question is asking for is:

    28 units to make the same $15,400 in revenue as the 11 units we were given.

  • 1 month ago

    R = 1642x - 11x² - x³

    first check that 11 gives you $15400

    R = 1642•11 - 11•121 - 1331 = 15400

    ok

    1642x - 11x² - x³ = 15400

    solve for x

    graphically, the + solutions are 11 and 28

    so the answer is 28

  • 1 month ago

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  • 1 month ago

    yes the awnser is 15462$

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