Intermediate Microeconomics: Cost Minimization

I introduce the firm's cost minimization problem, discuss isocosts, and finding the optimal configuration of inputs by selecting the bundle that corresponds to the lowest isocost that crosses the isoquant corresponding to the required level of output. Then I go through our 'recipe book' for solving cost minimization problems for perfect complements, perfect substitutes, and cobb-douglas isoquants. My error on the perfect substitutes costs example was thinking it was wrong on the slide. Indeed with r=9/2 and w=3, the costs of using 12 units of labor and 2 units of capital is: 3*12 + 4.5*2 = 36+9=45 as listed on the slide!