Korean electronic chip manufacturer has a production function given by q = L^0.5K^0.5. 

a. Use Excel to determine the amount of capital, K, needed to produce 10 units of output for each value of labor, L, starting from L = 2 and going to L = 20 in increments of 1. Plot this isoquant. (Hint: The formula for that isoquant is 10 = L^0.5K^0.5. Squaring both sides of this equation, we obtain 100 = LK. Dividing both sides of the equation by L, we learn that K=100/L. ) 

b. Use Excel to determine the cost of each of these combinations of labor and capital if the wage rate, w, and the cost of capital, r, are each $30 per unit. Which combination of inputs minimizes the cost of producing 10 units of output? 

c. The slope of the isoquant is −100/L². Calculate the slope of the isoquant for each combination of inputs. The slope of the isocost line is −ω/r = −30/30 = −1. Verify that the cost minimizing input combination occurs where the slope of the isoquant equals the slope of the isocost line. Draw the isoquant and the isocost line and show that they are tangent at the cost-minimizing combination of inputs.