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 thefollowing function:
S = 20L0.3C 0.7
In this formula L represents the units of labor inputand 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 muchlabor and capital are needed in order to produce 50,000 tons ofsteel at minimum cost. |
| | Min | L | + | C | | | L0.3C 0.7 | | - Select your answer -??<>=Item 4 | | | | L, C | - Select your answer -??<>=Item 6 | |
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| (b) | Solve the optimization problem you formulated in part a. Hint:When using Excel Solver, start with an initial L > 0and C > 0. |
| If required, round your answers to two decimal places. |
| L = $ |
| C = $ |
| Cost = $ |
