Final answer:
The marginal product of input x₁ when x₂ = 34 in the production function y = 8x₁x₂ is 272.
Step-by-step explanation:
To find the marginal product of input x₁ when x₂ = 34, we differentiate the production function y = 8x₁x₂ with respect to x₁.
Taking the partial derivative of y with respect to x₁ while keeping x₂ constant, we get:
∂y/∂x₁ = 8x₂
Substituting x₂ = 34, we have:
∂y/∂x₁ = 8(34) = 272
Therefore, the marginal product of input x₁ when x₂ = 34 is 272.