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10. Janif consumes two goods (Good A and Good B). The utility function is represented as...

10. Janif consumes two goods (Good A and Good B). The utility function is represented as follows: ? = ?(?, ?) = 40?^0.5?^0.5 . The price is good A is $20 and price of good B is $5. Janif earns a weekly income of $600 and does not save. Solve for optimal consumption bundle for Janif using Lagrangian multiplier method. Show all working.

11. Jone consumes apples (A) and oranges (O). His utility function is as follows, ?(?,?) = ?^2?^2. The price of apples is $2 and oranges is $1. Jone has a weekly income of $12. Use the Lagrangian multiplier method to solve for optimal consumption bundle for Jone. Show all working.

12. A firm purchases capital (K) at $18 per unit and pays it workers (L) wage rate of $8 per hour. The production function of the firm is Q = 24K^0.6L^0.3 . Determine the maximum level of output the firm can produce given a budget of $50000.Use the Lagrangian method. Show all working.

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