Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function:
S = 20L0.30C 0.70
In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100.
a. Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost.
b. Solve the optimization problem you formulated in part (a). Hint: Use the Multistart option as described in Appendix 8.2. Add lower and upper bound constraints of 0 and 5000 for both L and C before solving.
Text Book: An Introduction to Management Science: Quantitative Approaches to Decision. By David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey Camm, James Cochran.