Question 1 (Cost Minimization). Suppose you own a computer company and are deciding where to locate your production plant. You have narrowed your choices down to two locations, San Francisco and Sacramento. In order to produce computers, you need labor (x₁) and capital (x₂). Your production function at each plant is identical and equal to:

f(x₁, x₂)= x₁^1/2*x₂^1/2 or alternatively f(L, K)= L^1/2*K^1/2

At the San Francisco plant, the price of labor (w₁) is 70 and the price of capital (w₂) is 70. At the Sacramento plant, the price of labor (w₁) is 60 and the price of capital (w₂) is 80 You can sell computers at $1,000 each.

a) Suppose you would like to produce 100 computers. Compute optimal inputs (x₁ and x₂ needed to produce 100 computers in the least costly way) in both locations. You may use either the Lagrange method or your intuition.

b) In which city would you locate your plant? In other words, in which city are profits greater?