Hello! Kindly provide detailed analysis and proof. Thanks!

1. 8 points Is the following production function characterized by increasing, constant, or decreasing returns to scale? Show rigorously! Q = 49/025 K-0.75 2. 12 points Elodie has a factory that produces widgets via the following production tech- nology: W = 500103406 where W is the output of widgets, L is labor, A is capital. The wage is $10 per unit of labor used, the rental rate of capital is $0.50 per unit of cap- ital employed. If Elodie wishes to produce as many widgets as possible using the $2000 received from the government to support the business during the coronavirus pandemic, how should the budget be split between labor and capital?3. Zume Pizza uses a combination of automation and labor to create their pizzas. Suppose their production process is governed by: Q = min{aL, 10K"} where L is the amount of labor, K is the amount of capital, and o > 0. Assume the rental rate of capital is $10. (a) 8 points What is the lowest cost to produce 240 pizzas assuming the wage is w, the rental rate of capital is $10, and for now assuming o = w? (b) 8 points Suppose Zume updates its production process to Q = al + 10K where L is the amount of labor, K is the amount of capital, and a > 0. Assume the rental rate of capital is $10. If we observe that Zume Pizza has produced 240 pizzas using a fully automated production process what can we conclude about the relationship between or and the wage? (c) 4 points How much does it cost Zume Pizza to produce 240 pizzas using the fully automated process