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Cost, revenue, and profit are in dollars and x is the number of units.

Suppose that the marginal revenue for a product is MR=1800 and the marginal cost MC=60sqrt(x+4), with a fixed cost of $900.
Find the profit or loss from the production and sale of 5 units.

User Djibe
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1 Answer

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Final answer:

The profit or loss from the production and sale of 5 units can be calculated by subtracting the total cost from the total revenue. The profit from the production and sale of 5 units is $8898.

Step-by-step explanation:

The profit or loss from the production and sale of 5 units can be calculated by subtracting the total cost from the total revenue. The marginal revenue for the product is MR=1800, and the marginal cost MC=60√(x+4), with a fixed cost of $900. To find the profit or loss from the production and sale of 5 units, we need to calculate the total cost and total revenue for that level of output.

Given that the marginal cost function is MC=60√(x+4), we can substitute x=5 to find the marginal cost at 5 units. MC=60√(5+4)=60√(9)=180.

The total cost can be found by integrating the marginal cost function over the range of 0 to 5 units: TC = ∫(0,5) 60√(x+4) dx. After integrating, we get TC = 2(5√(9)+36) = 2(15+36) = 102.

The marginal revenue is constant at MR=1800, so the total revenue is TR = MR × x = 1800 × 5 = 9000.

Therefore, the profit or loss from the production and sale of 5 units is given by the equation Profit = TR - TC = 9000 - 102 = 8898 dollars. So, the profit from the production and sale of 5 units is $8898.

User Abhy
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