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A catering firm has a fixed cost of 753 units and a variable cost of 196q per unit where q denotes the output. Find the value of q if the marginal cost is 93. Note: Write your answer rounded to one decimal position.

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Final answer:

The given cost function indicates a constant marginal cost of 196 per unit, and it is not possible to find a value of 'q' where the marginal cost is 93 with the information provided. Additional information might be necessary to proceed with this calculation.

Step-by-step explanation:

Finding the Output (q) when Marginal Cost is Given

To find the value of q for which the marginal cost is 93, we would need to differentiate the total cost function with respect to q and set it equal to 93. The total cost function for a firm with a fixed cost and a variable cost that depends on the output level q is given by the sum of fixed costs and variable costs. In this case:

Total Cost = Fixed Cost + Variable Cost = 753 + 196q

The marginal cost is the derivative of the total cost function with respect to q. Therefore:

Marginal Cost (MC) = d(Total Cost)/dq = d(753 + 196q)/dq = 196

However, we are given that the marginal cost is 93, not 196. Therefore, it seems there might be a misunderstanding because with the information provided, the marginal cost remains at a constant 196 per additional unit produced since it's simply the coefficient of q in the variable cost expression. If there are no additional pieces of information, such as discounts or increasing costs after a certain quantity, we cannot equate the marginal cost to 93 with the given cost structure.

If you have additional details that might affect the marginal cost, please provide them so we can accurately calculate the value of q.

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