Final answer:
a. The current revenue can be found by substituting x=70 in the revenue equation. b. The revenue increase can be calculated by subtracting the current revenue from the revenue when 74 chairs are sold. c. The marginal revenue when 70 chairs are sold daily can be found by evaluating the derivative of the revenue function at x=70. d. The estimated revenue for each day can be found by adding the marginal revenue to the current daily revenue.
Step-by-step explanation:
a. To find the current daily revenue, we need to substitute the value of x with 70 in the revenue equation R(x)=0.004x³+0.04x²+0.6x. So, R(70)=0.004(70)³+0.04(70)²+0.6(70). Solve this equation to find the current daily revenue.
b. To find how much the revenue would increase if 74 lawn chairs were sold each day, we need to subtract the current daily revenue from the revenue when 74 lawn chairs are sold. So, Revenue Increase = R(74) - R(70).
c. To find the marginal revenue when 70 lawn chairs are sold daily, we need to find the derivative of the revenue function with respect to x and evaluate it at x=70. The derivative of the revenue function is MR(x) = 0.012x² + 0.08x + 0.6. Substituting x=70 in this equation will give us the marginal revenue.
d. To estimate R(71), R(72), and R(73), we can use the marginal revenue calculated in part c. We can add the marginal revenue to the current daily revenue to get the estimated revenue for each day. For example, R(71) ≈ R(70) + MR(70).