Question: a) Explain Linear Programming (LP), and describe its assumptions, and model components. What are the fundamental requirements for being qualified as a Linear Programming problem?

a) Explain Linear Programming (LP), and describe

a) Explain Linear Programming (LP), and describe its assumptions, and model components. What are the fundamental requirements for being qualified as a Linear Programming problem? Also, discuss optimization in terms of Maximum and Minimum objective functions. b) A carpenter makes book shelves and desks. Each shelf requires 2 hours for carpentry and 4 hours painting. The company has a maximum of 60 hours for carpentry and 40 hours for painting available each week and they make a profit of $16 per shelf and $42 per desk. How many shelves and how many desks should the carpenter make? Plot a graph and show feasible regions and optimal point and calculate the optimal profit. (Hint: Maximize the objective function)

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