1. Find the maximum value ofsubject to the constraint 2x+4y subject to the constraint x²+2y²=300.
2. Your firm has recently won a contract to produce1000units of goods per day. The firm uses labour and capital to produce the good.

The quantity of labour per day,L is measured in hours and the wage is 10 per hour.

The quantity of capital,K, is measured in machine-hours and the price per machine hour is 40.

The production function that describes the relationship between the amounts of labour and capital, and the quantity of the good produced is, q=20(LK)^1/2.

1. Write down the total cost per day as a function of L and K
2. Find the amount of labour and capital to use to minimise the cost of producing 1000 units per day.

The CEO of your firm wants to know if it is feasible to increase its productivity given that it is currently working at the levels found in part b. In what ratio shouldLandKbe increased in order to increase productivity most efficiently?