Solve the following LPP graphically:
Maximize:
$
subject to the constraints:$
$
$
b) Find all values of k for which the vectors:$
are linearly independent.
The constraints are first plotted in the first quadrant. The line (4x_1+3x_2=12) cuts the axes at ((3,0)) and ((0,4)). The line (6x_1+18x_2=36), or equivalently (x_1+3x_2=6), cuts the axes at ((6,0)) and ((0,2)). With (x_1,x_2\ge0), _____ ___ ___ ____ ________ _________ _____ _____ _______ ____ ____ __________.
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_____ ______ ___ _____ ________.
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______ ___ ____ _____ _____ __________ _________ ______ ______ __________.
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_____ _________ ____ __________ _____ ___ __________ ______.
___ ____ ___ __________ __________ ____ _______ ________ _____ _________ __________.
_______ ________ ______ _________ ______ ______ ________ _______ _____ ____.
_________ _________ ___ _______ ___ ___ _________ ________ __________ ________ ____.
_______ ____ ______ ______ __________.
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Solve the following LPP graphically:
Maximize:
$
subject to the constraints:$
$
$
b) Find all values of k for which the vectors:$
are linearly independent.
Write the LPP formulation of the following transportation problem:
| Destination | Supply | |||
|---|---|---|---|---|
| $D_1$ | $D_2$ | $D_3$ | ||
| Source $O_1$ | 10 | 18 | 12 | 200 |
| Source $O_2$ | 15 | 17 | 9 | 300 |
| Source $O_3$ | 13 | 15 | 7 | 500 |
| Requirement | 400 | 200 | 400 |
Using matrix – minima method, find the initial basic feasible solution of the following transportation problem:
Hence find the optimal solution.
b) Check whether the following set is convex:
) निम्नलिखित दो खिलाड़ी शून्य योग खेल को प्रमुखता सिद्धांत द्वारा खेल में समानीत कीजिए और इस प्रकार खेल को हल कीजिए।
A company makes two kinds of leather belts. Belts A is high quality belt and belt B is of lower quality. The respective profits on A and B are ₹ 4 and ₹ 3 per belt. The production of each type A requires twice as much time as a belt. The production of each type of type B, and if all belts were of type B, the company could make 1000 belts per day. The supply of leather is sufficient for only 800 belts per day (both A
and B combined). Belt A require a fancy buckle and only 400 buckles per day are available. There are only 700 buckles a day available for belt B. What should be the daily production of each type of belt? Formulate this problem as an LP model and solve it by the graphical method.
b) Find the initial basic feasible solution of the following transportation problem using North-West Corner method.
) Using matrix – minima method, find the initial basic feasible solution of the following transportation problem:
Hence find the optimal solution.
b) Check whether the following set is convex:
$
wo breakfast food manufacturers ABC and XYZ are competing for an increased market share. The pay-off matrix, shown in the following table, describes the increase in market share for ABC and decrease in market share of XYZ. Determine optimal strategies for both the manufacturers and the value of the game.
b) Find all the basic feasible solutions of the following system of linear equations:
$
$
$
Check if any of them is degenerate solution. Justify your answer.