Problem 1. A huge type of printing machine for producing fancy business cards stamped with golden foil features takes two people to operate. Two operators print 500 fancy business cards per hour using the machine. One single operator alone can't print a single card with the machine. Three people using the machine print the same number as two people because there is no way for the third person to do anything useful. The rm can hire operators at a wage rate of a; per hour and can hire machines at a rental rate of 1' per hour. Assume workers can be hired and machines can be rented for any fractional amounts. For example, you may hire a worker for 10 minutes and pay them 10/6, or you could rent a machine for 30 seconds and pay r/ 120. (1.1) Write a mathematical expression for f (L, K ), the maximum number of busi- ness cards that can be produced per hour, when you hire L units of labor (measured in person-hours) and K units of capital (measured in machine- hours). (1.2) With L on the horizontal axis, and K in the vertical axis, draw the isoquant f(L, K) = 2000. (1.3) What is the marginal product of L when (L,K) = (4, 2)? (1.4) What is the marginal product of K when (L, K) = (10,2)? (1.5) What is the cheapest combination of K and L to produce 20000 cards per hour? Write an expression for the cost in terms of w and r. (1.6) Does this technology exhibit decreasing, constant or increasing returns to scale? Show the algebra by scaling all inputs by a factor of t > 1