Applying the least-cost condition (LCC)

You are the manager of the Axes Corporation which uses labor (L) and capital (K) to produce X and Y axes for course diagrams. The price of workers is $5 per unit and the price of capital is $10 per machine. You have orders to produce 300 axes and have the following information about your production:
Case Q K L MPL Q K L MPK TC300 MPL/PL MPK/PK 1 298 6 119 2 284 5 120     0.4   300 6 120 300 6 120 2 295 30 71   296 29 72         300 30 72 300 30 72 3 297 15 89   294 14 90         300 15 90 300 15 90
Each case above corresponds to either point a, b, or b' in the diagram to the right. Decide which case goes with which point, and then label the diagram with each of the following numerical values:     (1) quantity of L     (2) quantity of K     (3) TC     (4) L-axis endpoint of the isocost line     (5) K-axis endpoint of the isocost line, and     (6) MRTS. Similar information for point c is provided as an illustration.