How To Solve Linear Programming Word Problems

How To Solve Linear Programming Word Problems-52
Vertices: A at intersection of \( x y = 20000 \) and \( y = 0 \) , coordinates of A: (20000 , 0) B at intersection of \( x y = 17000 \) and \( y=0 \) , coordinates of B: (17000 , 0) C at intersection of \( x y = 17000 \) and \( x = 2y \) , coordinates of C : (11333 , 5667) D at at intersection of \( x = 2y \) and \( x y = 20000 \) , coordinates of D: (13333 , 6667) Evaluate the return R(x,y) = 1000 - 0.03 x - 0.01 y at each one of the vertices A(x,y), B(x,y), C(x,y) and D(x,y).

Vertices: A at intersection of \( x y = 20000 \) and \( y = 0 \) , coordinates of A: (20000 , 0) B at intersection of \( x y = 17000 \) and \( y=0 \) , coordinates of B: (17000 , 0) C at intersection of \( x y = 17000 \) and \( x = 2y \) , coordinates of C : (11333 , 5667) D at at intersection of \( x = 2y \) and \( x y = 20000 \) , coordinates of D: (13333 , 6667) Evaluate the return R(x,y) = 1000 - 0.03 x - 0.01 y at each one of the vertices A(x,y), B(x,y), C(x,y) and D(x,y).

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Each month a store owner can spend at most $100,000 on PC's and laptops.

A PC costs the store owner $1000 and a laptop costs him $1500.

How many bags of food A and B should the consumed by the animals each day in order to meet the minimum daily requirements of 150 units of proteins, 90 units of minerals and 60 units of vitamins at a minimum cost?

Let x be the number of bags of food A and y the number of bags of food B.

Several word problems and applications related to linear programming are presented along with their solutions and detailed explanations.

Methods of solving inequalities with two variables, system of linear inequalities with two variables along with linear programming and optimization are used to solve word and application problems where functions such as return, profit, costs, etc., are to be optimized. The store owner pays and for each one unit of toy A and B respectively.The hard part is usually the word problems, where you have to figure out what the inequalities are.So I'll show how to set up some typical linear-programming word problems.How many of each type of tables should be produced in order to maximize the total monthly profit?Let x be the number of tables of type T1 and y the number of tables of type T2.A bag of food A costs and contains 40 units of proteins, 20 units of minerals and 10 units of vitamins.A bag of food B costs and contains 30 units of proteins, 20 units of minerals and 30 units of vitamins.From the graph, I can see which lines cross to form the corners, so I know which lines to pair up in order to verify the coordinates.I'll start at the "top" of the shaded area and work my way clockwise around the edges: Given the inequalities, linear-programming exercise are pretty straightforward, if sometimes a bit long.Hence the company needs to produce 2300 tables of type T1 and 600 tables of type T2 in order to maximize its profit.A farmer plans to mix two types of food to make a mix of low cost feed for the animals in his farm.

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