A young couple is living together and sometimes orders pizza. The pizza can either be self-made (Q₁) or ordered (Q₂). Assume that the couple has a pizza budget of $150 for pizza during a month.

a)What is the couples' monthly budget condition for pizza? What is the slope of the budget condition?

b)Assume that the couple has a utility function over Q₁ and Q₂ given by: U(Q₁, Q₂) = Q₁^0.45 * Q₂^0.3. What is their optimal fit, what will they as utility maximizers choose of Q₁ and Q₂?

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a) I understand the approach and how to solve this and also have calculated the answer, which is 50Q₁ + 150Q₂ = 1500, Q₁ = 30 - 3Q₂ and Q₂ = 10 - 1/3Q₁

b) I have the answer which is Q₁ = 18 and Q₂ = 4, and see that the approach is an equation set. However, I don't have the full calculation and have trouble with solving it myself