31. The daily cost, C(x), for a company to produce x microscopes is given by the equation C(x) = 300 + 10.5x. What is the cost of producing 50 microscopes?
Answer: D
The cost of producing 50 microscopes is $825.
To find the cost of producing 50 microscopes, we can substitute x with 50 in the equation C(x) = 300 + 10.5x. This gives us C(50) = 300 + 10.5(50) = 300 + 525 = 825.
A) $41,250
This option is incorrect as it significantly overestimates the cost. The calculation does not align with the equation provided; substituting 50 into the equation does not yield this figure.
B) $360.50
This option is also incorrect. It underestimates the cost because when substituting x = 50 into the equation C(x) = 300 + 10.5x, the result is much higher than $360.50.
C) $15,525
This option is incorrect as well. The figure is too high and does not result from substituting 50 into the cost equation, which clearly indicates a different total.
D) $825
This option is correct. When substituting x = 50 into the equation C(x) = 300 + 10.5x, the calculation gives C(50) = 300 + 525 = 825, confirming this as the accurate cost.
Conclusion
The correct answer is $825 because it is the result of the proper calculation using the given cost equation. All other options fail to reflect the accurate cost derived from substituting the value of x into the equation, making them incorrect.