(LO4) A firm's marginal cost function is MC=3Q^2+10Q Find the total cost of producing 12 goods if the fixed costs are 10. a). 94 b). 940 c). 1060 d). 1728 c). 1798

To find the total cost of producing 12 goods, we need to integrate the marginal cost function with respect to the quantity and then add the fixed costs.<br /><br />Given the marginal cost function:<br />\[ MC = 3Q^2 + 10Q \]<br /><br />The total cost function \( TC \) can be found by integrating the marginal cost function:<br />\[ TC = \int (3Q^2 + 10Q) \, dQ \]<br /><br />Integrating term by term:<br />\[ TC = \int 3Q^2 \, dQ + \int 10Q \, dQ \]<br />\[ TC = 3 \int Q^2 \, dQ + 10 \int Q \, dQ \]<br />\[ TC = 3 \left( \frac{Q^3}{3} \right) + 10 \left( \frac{Q^2}{2} \right) \]<br />\[ TC = Q^3 + 5Q^2 \]<br /><br />Now, we need to evaluate this total cost function at \( Q = 12 \) and then add the fixed costs of \$10.<br /><br />\[ TC(12) = 12^3 + 5 \cdot 12^2 \]<br />\[ TC(12) = 1728 + 5 \cdot 144 \]<br />\[ TC(12) = 1728 + 720 \]<br />\[ TC(12) = 2448 \]<br /><br />Finally, adding the fixed costs:<br />\[ Total \, Cost = TC(12) + Fixed \, Costs \]<br />\[ Total \, Cost = 2448 + 10 \]<br />\[ Total \, Cost = 2458 \]<br /><br />Therefore, the correct answer is:<br />c). 1798