Final answer:
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.