4. Formulate the following as a lnear pagrammny prublem A state wants to plan ct

Question

4. Formulate the following as a lnear pagrammny prublem A state wants to plan cts electricty capacity for te next T year l state has a forecast of de mega watts of demaund for electrica durung year t.1-..,?.whde existing capaag, eshich is in oil-fired plants, hat will not be retired and will a available during year t à e Ten an two alternatives for expanding electrie capacity: Coal- firedl or Nuclear power plants There a capital cost ef ct per Mega watt of cool fired Capaidy that becomes operational at ihe biginning of year t,?e Correspon- dig capital cost fer nuclear pover plant Re For various political and safety easons, et has heen decided that no more than 20% of He total afact Should ever be nuclear. Coal plants last for 2o yeas tohile nuclear plants last for 4s years. A least cast Capacdy expansion u desired

Explanation / Answer

Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polyhedron where this function has the smallest (or largest) value if such a point exists.

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