Question

4. a) Other than the joy it may have been to create your game, one of the most important things is
the economic research that goes behind your game. The cost, C(n), to make your game is
modeled by the equation C(n) = 0.156- 0.6n + 3
in millions of dollars, where n is the
number of products produced per hour in thousands Determine the minimum production cost.

Answer 1

9514 1404 393

Answer:

  about 2.423 million dollars

Step-by-step explanation:

We assume your equation is supposed to be ...

  C(n) = 0.156n² -0.6n +3

This describes a parabola that opens upward. The minimum cost will be found at the vertex of the parabola.

The n-coordinate of the vertex is* ...

  n = -b/(2a) = -(-0.6)/(2(0.156)) = 0.6/0.312 = 25/13 ≈ 1.92308

The C-coordinate of the vertex is ...

  C(25/13) = (0.156×25/13 -0.6)(25/13) +3 = 63/26 ≈ 2.42308

The minimum production const is about 2.423 million dollars.

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* In this equation for the vertex, the 'a' and 'b' refer to the coefficients of a quadratic in standard form: ax² +bx +c.