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Gerardo's Geraniums is a flower farm specializing in the production of cut geraniums. The cut geraniums market is a perfectly competitive market. Gerardo has hired an economist to determine his total cost function, which the economist reports as:

\[ TC(q) = 50,000 + 0.0025q^2 \]

where \( q \) is the number of cut flowers Gerardo's Geraniums produces.

Determine Gerardo's Geraniums marginal cost of supplying an additional cut geranium (carefully, enter your response as an algebraic expression, using the proper notation in the proper format). Suppose that the price of a cut is $2.00. Determine if Gerardo's Geraniums will supply cut geraniums.

Answer :

Final answer:

The marginal cost of supplying an additional cut geranium is MC(q) = 0.005q.

Explanation:

The marginal cost of supplying an additional cut geranium for Gerardo's Geraniums can be found by taking the derivative of the total cost function with respect to q. The derivative of 50,000+0.0025q^2 with respect to q is 0.005q. So, the marginal cost function for Gerardo's Geraniums is MC(q) = 0.005q.

If the price of a cut geranium is $2.00, Gerardo's Geraniums will supply cut geraniums as long as the marginal cost of producing an additional cut geranium is less than or equal to $2.00. Therefore, Gerardo's Geraniums will supply cut geraniums at any quantity of q where MC(q) <= $2.00.

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Rewritten by : Barada

Final answer:

The marginal cost of supplying an additional cut geranium for Gerardo's Geraniums is MC(q) = 0.005q. Gerardo's Geraniums will supply cut geraniums as long as the marginal cost is less than $2.00.

Explanation:

To find Gerardo's Geraniums marginal cost of supplying an additional cut geranium, we need to take the derivative of the total cost function, TC(q) = 50,000 + 0.0025q², with respect to q.

First, let's find the derivative of the constant term, 50,000. The derivative of a constant is zero, so it does not affect the marginal cost.

Next, let's find the derivative of the quadratic term, 0.0025q². Using the power rule of differentiation, the derivative of q² is 2q. Multiplying this by the coefficient 0.0025, we get 0.005q.

Therefore, the marginal cost function is MC(q) = 0.005q.

Now, let's determine the quantity of cut geraniums Gerardo's Geraniums will supply. We compare the marginal cost, MC(q), to the price of a cut geranium, which is $2.00.

If the marginal cost is less than $2.00, Gerardo's Geraniums will supply an additional cut geranium. If the marginal cost is equal to or greater than $2.00, Gerardo's Geraniums will not supply any additional cut geraniums.

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