21. The daily cost, C(x), tor 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 total cost of producing 50 microscopes, we substitute x with 50 in the equation C(x) = 300 + 10.5x. This results in C(50) = 300 + 10.5(50), which equals $825.
A) $41,250
This option is incorrect because it significantly overestimates the cost. The calculation of C(50) = 300 + 10.5(50) results in a total of $825, not anywhere near $41,250.
B) $360.50
This option is incorrect as it also underestimates the total cost of producing 50 microscopes. The computation shows that the cost should be $825, making this option not viable.
C) $15,525
This choice is incorrect as it miscalculates the cost based on the given equation. The proper calculation shows that producing 50 microscopes costs $825, not $15,525.
D) $825
This option is correct as it accurately represents the total cost calculated from the equation. By substituting 50 into C(x), we find that C(50) = 300 + 10.5(50) = $825, confirming its correctness.
Conclusion
The correct answer, $825, is derived directly from the cost equation by substituting the appropriate value for x. All other options fail because they either overestimate or underestimate the total cost based on the given formula. Therefore, $825 is definitively the accurate cost for producing 50 microscopes.