b. Find the marginal cost, marginal revenue, and marginal profit when 70 parkas are produced and sold using the formulas \( C(x+1)-C(x), R(x+1)-R(x) \), and \( P(x+1)-P(x) \). Marginal cost: \( \$ 0.8 \) Marginal revenue: \( \$-0.4 \) Marginal profit: \( \$ \) c. Use derivatives to estimate the marginal cost, marginal revenue, and marginal profit when 70 parkas are produced and sold. Marginal cost: \( \$ \) Marginal revenue: \( \$ \)

When calculating the marginal profit, you can find it by subtracting the marginal cost from the marginal revenue. Using the provided values: \( \text{Marginal Profit} = \text{Marginal Revenue} - \text{Marginal Cost} \). Therefore, with a marginal cost of \( \$0.8 \) and marginal revenue of \( \$-0.4 \), the marginal profit would be \( -0.4 - 0.8 = -1.2 \). So, the marginal profit is \( \$-1.2 \). To estimate the marginal cost, revenue, and profit using derivatives, recall that the derivative gives the rate of change at a point. If \( C'(x) \) represents the derivative of the cost function, \( R'(x) \) for revenue, and \( P'(x) \) for profit, you'd evaluate these derivatives at \( x = 70 \). Assuming you've derived these functions prior to this, substituting \( x = 70 \) will yield the estimates for marginal cost and marginal revenue at that production level; however, you'll need their specific expressions to perform the calculation.