A company's marginal cost function is MC=21x^4/3-6x^1/2+50, where x is the number of units, and fixed costs are $3000. Find the cost function.
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The marginal cost function is the change in cost incurred for producing an additional unit.
MC = `21x^(4/3)-6x^(1/2)+50`
The cost function is `int MC dx`
= `int 21x^(4/3)-6x^(1/2)+50 dx`
= `9*x^(7/3)-4*x^(3/2)+50*x + C`
As the fixed cost is $3000, C = 3000
The cost function of the company is `9*x^(7/3)-4*x^(3/2)+50*x + 3000`
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