Cat 1 Solved, N o Plagiarism

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ASSIGNMENT
a) Define linear programming giving its mathematical expression 3mks
b) Answer True or False for each of the following statements on fundamental theorem of LP
4mks
i. Although any CPF (corner point feasible) solution can be chosen to be the initial CPF
solution, the simplex method always chooses the origin.
ii. An LP problem cannot handle variables that could be negative.
iii. If there is no leaving variable in a column selected for an entering basic variable, then the
objective function is unbounded.
iv. If the final tableau of the simplex method applied to LP has a nonbasic variable with a
coefficient of 0 in row 0, then the problem has multiple solutions.
c) Consider the following LPP
Minimize
2π‘₯1 + 3π‘₯2
Subject to the constraints π‘₯𝑖 β‰₯ 0, 𝑖 = 1,2 and
π‘₯1 + 2π‘₯2 β‰₯ 4
π‘₯1 + π‘₯2 β‰₯ 3
Convert the problem to a maximization problem 4mks
a) (Medicine) A patient in a hospital is required to have at least 84 units of drug A and 120 units of
drug B each day. Each gram of substance M contains 10 units of drug A and 8 units of drug B, and
each gram of substance N contains 2 units of drug A and 4 units of drug B. Now suppose that both
M and N contain an undesirable drug C, 3 units per gram in M and 1 unit per gram in N. How many
grams of substances M and N should be mixed to meet the minimum daily requirements at the
same time minimize the intake of drug C? How many units of the undesirable drug C will be in this
mixture?
i. Formulate the problem of how much of each product to produce as a linear
program.
8mks
ii. Solve this linear program graphically. 6mks

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ASSIGNMENT
a) Define linear programming giving its mathematical expression 3mks
b) Answer True or False for each of the following statements on fundamental theorem of LP
4mks
i. Although any CPF (corner point feasible) solution can be chosen to be the initial CPF
solution, the simplex method always chooses the origin.
ii. An LP problem cannot handle variables that could be negative.
iii. If there is no leaving variable in a column selected for an entering basic variable, then the
objective function is unbounded.
iv. If the final tableau of the simplex method applied to LP has a nonbasic variable with a
coefficient of 0 in row 0, then the problem has multiple solutions.
c) Consider the following LPP
Minimize
2π‘₯1 + 3π‘₯2
Subject to the constraints π‘₯𝑖 β‰₯ 0, 𝑖 = 1,2 and
π‘₯1 + 2π‘₯2 β‰₯ 4
π‘₯1 + π‘₯2 β‰₯ 3
Convert the problem to a maximization problem 4mks
a) (Medicine) A patient in a hospital is required to have at least 84 units of drug A and 120 units of
drug B each day. Each gram of substance M contains 10 units of drug A and 8 units of drug B, and
each gram of substance N contains 2 units of drug A and 4 units of drug B. Now suppose that both
M and N contain an undesirable drug C, 3 units per gram in M and 1 unit per gram in N. How many
grams of substances M and N should be mixed to meet the minimum daily requirements at the
same time minimize the intake of drug C? How many units of the undesirable drug C will be in this
mixture?
i. Formulate the problem of how much of each product to produce as a linear
program.
8mks
ii. Solve this linear program graphically. 6mks

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