The average cost for a printing shop at UGBS is given as: 𝐶 = −1000𝑞 + 6.75𝑞 2 − 10340 Where q is the quantity output. Find the marginal cost when quantity is 2000
Question
The average cost for a printing shop at UGBS is given as: 𝐶 = −1000𝑞 + 6.75𝑞 2 − 10340 Where q is the quantity output. Find the marginal cost when quantity is 2000
Solution
The marginal cost is the derivative of the total cost function.
The total cost function given is: C = -1000q + 6.75q^2 - 10340
To find the derivative of this function, we apply the power rule, which states that the derivative of x^n is n*x^(n-1).
The derivative of -1000q is -1000. The derivative of 6.75q^2 is 2*6.75q = 13.5q. The derivative of a constant, like -10340, is 0.
So, the derivative of the cost function, which represents the marginal cost, is: MC = -1000 + 13.5q
To find the marginal cost when the quantity is 2000, we substitute q = 2000 into the marginal cost function:
MC = -1000 + 13.5*2000 = 26000
So, the marginal cost when the quantity is 2000 is 26000.
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