Lagrange Interpolating Polynomial

We are given the Lagrange polynomial in the form: P_n(x)= y_0*L_0(x)+...+y_n*L_n(x) and y_i = f(x_i) and L_i(x)= ((x-x_0)***(x-x_n)) / ((x_i-x_0)***(x_i-x_n)). We must show that L_0(x) + ... + L_n(x) = 1 for all x and n=3. Later we are to generalize this for all n>0. But let's just focus on n=3 for now; I may be able to get the rest later. We know that each L_i(x) equals the Kronecker Delta, i.e. it is either 0 or 1. It is also proven that P_n(x_i)=y_i. From this I concluded that L_i(x)=1 only when x=x_i and zero otherwise. But if I choose any x other than x_0 to x_3, L_i(x) will be zero. Can I use P_n(x) and let every y_i = 1? Will this make the sum of the L's equal to 1?... click for more

Numerical Analysis

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Excel Solver - linear programming model.

Need help with the following problem, am stuck trying to set it up correctly. Can you help with the objective function and constraints, also the formulas for solver. The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several students of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assig... click for more

Transportation Model linear programming model. Need help setting up problem for Excel solver.

Having real problems setting up transportation problems in Excel's Solver. Please help with objective function, constraints, formulas, etc. Spreadsheet would be wonderful soI can see how to do it! The Krampf Lines Railway Company specializes in coal handling. On Friday APril 13, Krampf needed empty coal cars to be moved from three locations (Morgantown, Youngstown, and Pittsburgh) to four other locations. (Mill Valley, Coal Town, Junction City, and Limeburg). Using a railway city-to-city distance chart, the dispatcher constructs a mileage table for the preceding towns, as shown in the table. The table also shows the availablilities and requirements. Find the best shipment of coal cars to ... click for more

Need help with Excel Solver Linear Programming Model

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