Question

A certain electronics manufacturer found that the marginal cost C to produce x DVD/Blu-ray players can be found using the equation C = 0.04x² – 5x + 900. If the marginal cost were $1146, how many DVD/Blu-ray players were produced?

A) 36 players
B) 27 players
C) 64 players
D) 49 players

Answer 1

To find the number of DVD/Blu-ray players produced when the marginal cost is $1146, the equation C = 0.04x² – 5x + 900 is solved for x, resulting in x = 150 after factoring the quadratic equation, which means that none of the provided options are correct.

Step-by-step explanation:

To find the number of DVD/Blu-ray players produced when the marginal cost is $1146, we substitute $1146 for C in the marginal cost equation C = 0.04x² – 5x + 900 and solve for x:

1146 = 0.04x² – 5x + 900

0.04x² – 5x + 900 – 1146 = 0

0.04x² – 5x – 246 = 0

Now we solve the quadratic equation either by factoring, completing the square, or using the quadratic formula. If the quadratic can be factored, we find the values of x that make the equation true:

x² – 125x – 6150 = 0

(x - 150)(x + 41) = 0

So, x = 150 or x = -41. Since we cannot produce a negative number of players, we disregard the negative solution. Therefore, the manufacturer produced 150 DVD/Blu-ray players when the marginal cost was $1146, and none of the provided options (A, B, C, D) are correct.