A consumer has the following utility function

U (x₁, x₂) = x₁(x₂ + 4)

Prices of the two goods x₁ and x₂ respectively are p₁ and p₂ and the consumer has income m. We assume that all prices and income are strictly positive. Furthermore, throughout this question we assume that m > 4p₂.

(a) Find the consumer's MRS between the two goods (i.e., marginal utility of x₁ divided by marginal utility of x₂).

(b) Write down the equation for the consumer's budget line and the slope of the budget line where x₁ is on the horizontal axis and x₂ is on the vertical axis.

(c) Solve the consumer's optimization problem and express the demand for the two goods in terms of prices and income.