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?

Rationale

The cost of producing 50 microscopes is $825.

To find the cost of producing 50 microscopes, we can substitute x with 50 in the cost function C(x) = 300 + 10.5x. This calculation yields a total cost of $825, confirming that this is the correct answer.

A ($41,250) YOUR ANSWER

This option results from a misunderstanding of the cost function. If one mistakenly multiplies the number of microscopes by an incorrect rate, they might arrive at an inflated total. The correct approach involves substituting 50 into the given equation, leading to a much lower cost.

B ($360.50) YOUR ANSWER

This figure is incorrect as it may arise from an error in the basic arithmetic involved in the cost calculation. Substituting 50 into the equation C(50) = 300 + 10.5(50) correctly computes to $825, not $360.50, demonstrating a miscalculation.

C ($15,525) YOUR ANSWER

This choice appears to be the result of an incorrect multiplication of costs or an incorrect interpretation of the cost function. The formula clearly shows that the cost increases linearly with the number of microscopes produced, and substituting 50 should yield $825 rather than this inflated value.

D ($825) CORRECT

This is the correct calculation based on the cost formula. By substituting x = 50 into C(x) = 300 + 10.5(50), we get C(50) = 300 + 525 = 825, accurately reflecting the total cost for producing 50 microscopes.

Conclusion

The cost calculation for producing a given number of microscopes is critical for business operations. Here, using the formula C(x) = 300 + 10.5x, we determined that the total cost for producing 50 microscopes is $825. The other options reflect common miscalculations that ignore the structure of the equation, underscoring the importance of precise arithmetic in financial assessments.

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?

The cost of producing 50 microscopes is $825.

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