(a) The expansion path for Ivor’s Engines MAPs the optimal input combinations for each quantity Q. Here, points X, Y, and Z are the cost-minimizing input combinations given output levels Q = 10, Q = 20, and Q = 30, respectively.(b) The total cost curve for Ivor’s Engines is constructed using the isocost lines from the expansion path in panel a. The cost-minimizing input combinations cost $100, $180, and $300 at output levels Q = 10, Q = 20, and Q = 30, respectively.