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First, we need to find the total equity of the Red Zeppelin Corporation. The debt-equity ratio is given as \(3\), which means that the company has three times more debt than equity. Let's denote the equity with \(E\), and the debt with \(D\). We have: \[D = 3E\] The company's earnings for the year are \(\$ 140,000\). According to the residual dividend policy, the company will first use these earnings to cover their investment needs, and only the remaining amount will be distributed as dividends if applicable.

In order to find the maximum amount of capital spending possible without raising new equity, we can subtract the equity portion of the investment from the total earnings: \[CapitalSpending = Earnings - E\] Since we have the debt-equity ratio, we can express the equity portion of the investment as a fraction of the debt, which is \(D = 3E\): \[CapitalSpending = Earnings - \frac{D}{3}\] Now, plug in the given earnings amount: \[CapitalSpending = \$140,000 - \frac{D}{3}\] However, we do not have enough information to calculate an exact value for capital spending. We can only express it in terms of debt.

Next, we need to consider the planned investment outlays for the upcoming year, which are given as \(\$ 770,000\). Let's first check if the company will pay a dividend: If \(CapitalSpending \ge \$ 770,000\), then some or all the earnings will go towards investment, and the company will not pay a dividend: \[\$140,000 -\frac{D}{3} \ge \$ 770,000\] Solving for D: \[\frac{D}{3} \le \$ 140,000 - \$ 770,000 \rightarrow D \le 3(\$ 630,000) \rightarrow D \le \$ 1,890,000\] Since we do not have any information about the company's debt, we cannot determine whether Red Zeppelin will pay a dividend or not. If the inequality is true, then Red Zeppelin will not pay a dividend, but if it is false, we can calculate the dividend amount as follows: \[DividendsPaid = Earnings - CapitalSpendingUsedForInvestments\] Capital Spending Used for Investments is limited to Red Zeppelin's investment outlays and can be calculated using D.

Lastly, we must comment on whether Red Zeppelin maintains a constant dividend payout. A constant dividend payout policy means that the company pays a certain percentage of its profits as dividends each year. Since Red Zeppelin follows a strict residual dividend policy, the company will cover its investment needs with its earnings first, and only the remaining earnings will be distributed as dividends. This means that the dividend payout will vary depending on the company's investment needs, which can change from year to year. Therefore, we can conclude that Red Zeppelin does not maintain a constant dividend payout.