Math

posted by .

A manufacture of a certain commodity has estimated that her profit in thousands of dollars is given by the expression

-6x^2+30x-10

where x (in thousands) is the number of units produced. What production range will enable the manufacturer to realize a profit of a least $14,000 on the commodity?

  • Math -

    -6X^2 + 30X -10 = 14,
    -6X^2 + 30X - 24 = 0,
    Divide3 both sides by -6:
    X^2 - 5X + 4 = 0,
    (X-4)(X-1) = 0.
    X-4 = 0,
    X = 4.

    X-1 = 0,
    X = 1.

    Production Range: 1000 to 4000 Units.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. statistics

    A study was conducted to investigate the relationship between the cost, y (in tens of thousands of dollars), per unit of equipment manufactured and the number of units produced per run, x. The resulting equation for the line of best …
  2. Business Calculus

    A company has operating costs of $2000 per thousand items produced. Its revenue function can be modeled by the equation: R(x)=30x/(x+2)² , where x is measured in thousands of items produced, and C and R are measured in thousands of …
  3. algebra

    Annual profit in thousands of dollars is given by the function,p(x)=200square x-3 +10,000,where x is the number of items sold in thousands, x less than 3. describe the meaning of the numbers 3 and 10,000 in the formula. find the profit …
  4. Algebra

    Annual profit in thousands of dollars is given by the function, P(x) = 12x-100, where x is the number of items sold in thousands x ¡Ý 10. Will this profit function have a maximum if so what is it?
  5. Trig

    Dalco manufacturing estimate that its weakly profit, P, in hundreds of dollars,can be approximated by the formula P= -4x²+8x+7, where x is the number of units produced per week, in thousands. 1)How many units should the company produce …
  6. Math

    The monthly profit P, in thousands of pesos of a company can be estimated by the formula P(x)= -3x^2+30x+2, where x is the number of units sold per month. Find the number of units that must be sold by the company to maximize its profit …
  7. College Algebra

    Suppose that the price per unit in dollars of a cell phone production is modeled by p = $45 − 0.0125x, where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R = x · p. Find the production …
  8. Math

    The cost of producing x units of a certain commodity is given by P(x)=1000+ int(MC(s))ds from 0 to x, where P is in dollars and M(x) is marginal cost in dollars per unit. A. Suppose the marginal cost at a production level of 500 units …
  9. MATH PRECAL HELP

    Business. The profit, in thousands of dollars, for a product is p(X)=-x^2+140x-4700 where x is the production level in hundreds of units. Find the production level that maximizes the profit. Find the maximum profit. The maximum profit …
  10. Calculus

    The profit function for a computer company is given by P(x)=−x^2+36x−26 where x is the number of units produced (in thousands) and the profit is in thousand of dollars. a) Determine how many (thousands of) units must be produced …

More Similar Questions