五、將 1 大氣壓及溫度 30 °C 的空氣，以 20 m/s 的速度通入內徑為 1 cm 的恆溫鋼管內，鋼管長度為 2 m 且管壁溫度均維持在 105 °C，空氣出口溫度為 90 °C，試求其平均對流熱傳係數(空氣平均密度為 0.0012 g/cm³，平均比熱為 0.23 cal/g·°C)。(15 分)

3. James has a monopoly on a board game called "Fly High" and faces a demand curve given by \( Q_T = 100 - P \), where \( Q_T \) equals the combined total number of games produced per hour in the company's two factories (\( Q_T = q_1 + q_2 \)). If factory 1 has a marginal cost function given by \( MC_1 = q_1 - 5 \) and factory 2 has a marginal cost function given by \( MC_2 = 0.5q_2 - 5 \), how much total output will James choose to produce and how will he divide this output between its two factories in order to maximize profits? (10%)

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