The marginal cost function of manufacturing x units of a product is 5+16x – 3x2 . The total cost of producing 5 items is GHC500. Find the total cost
Question
The marginal cost function of manufacturing x units of a product is given by:
The total cost of producing 5 items is GHC500. Find the total cost.
Solution
To find the total cost of manufacturing x units of a product, we need to integrate the marginal cost function. The marginal cost function is the derivative of the total cost function, so to find the total cost function, we integrate the marginal cost function.
The marginal cost function is 5 + 16x - 3x^2.
∫(5 + 16x - 3x^2) dx = 5x + 8x^2 - x^3 + C
We know that the total cost of producing 5 items is GHC500. We can use this information to solve for C.
500 = 5(5) + 8(5)^2 - (5)^3 + C 500 = 25 + 200 - 125 + C 500 = 100 + C C = 500 - 100 C = 400
So, the total cost function is C(x) = 5x + 8x^2 - x^3 + 400.
Now, you can use this function to find the total cost of producing any number of units.
Similar Questions
The marginal cost function for producing x units is 3x2 – 200x +1500 rupees. Find the increase in cost if production is increasedfrom 90 to 100 units.
Use the following figure to answer the question below. The marginal utility of the third unit of X isMultiple Choice15 utils.2 utils.4 utils.5 utils.
e correct answerThe cost of 25 items is the same as the revenue by selling X items. Find X, if the profit made in the transaction is 25%?
Consider the following case: price is $100 and 20 units are sold, then price drops to $99 and 21 units are sold.Calculate the marginal revenue: $________.
Suppose a firm’s short-run production function is given by 𝑄𝑄 = 16𝐿𝐿0.8. What is the marginal product ofthe fourth worker?a) 36b) 10c) 49d) 1.85
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.