Plant food . A farmer can buy four types of plant food. Each barrel of mix A contains 30 pounds of phosphoric acid. 50 pounds of nitrogen, and 30 pounds of potash; each barrel of mix B contains 30 pounds of phosphoric acid. 75 Pounds of nitrogen, and 20 pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid. 25 pounds of nitrogen, and 20 pounds of potash; and each barrel of mix D contains 60 pounds of phosphoric acid. 25 pounds of nitrogen, and 50 pounds of potash. Soil tests indicate that a particular field needs 900 pounds of phosphoric acid, 750 pounds of nitrogen, and 700 pounds of potash. How many barrels of each type of food should the farmer mix together to supply the necessary nutrients for the field?
Plant food . A farmer can buy four types of plant food. Each barrel of mix A contains 30 pounds of phosphoric acid. 50 pounds of nitrogen, and 30 pounds of potash; each barrel of mix B contains 30 pounds of phosphoric acid. 75 Pounds of nitrogen, and 20 pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid. 25 pounds of nitrogen, and 20 pounds of potash; and each barrel of mix D contains 60 pounds of phosphoric acid. 25 pounds of nitrogen, and 50 pounds of potash. Soil tests indicate that a particular field needs 900 pounds of phosphoric acid, 750 pounds of nitrogen, and 700 pounds of potash. How many barrels of each type of food should the farmer mix together to supply the necessary nutrients for the field?
Solution Summary: The author calculates the quantity of each type of food that should be used to meet the requirement of a particular field.
Plant food. A farmer can buy four types of plant food. Each barrel of mix A contains
30
pounds of phosphoric acid.
50
pounds of nitrogen, and
30
pounds of potash; each barrel of mix
B
contains
30
pounds of phosphoric acid.
75
Pounds of nitrogen, and
20
pounds of potash; each barrel of mix
C
contains 30 pounds of phosphoric acid.
25
pounds of nitrogen, and
20
pounds of potash; and each barrel of mix
D
contains
60
pounds of phosphoric acid.
25
pounds of nitrogen, and
50
pounds of potash. Soil tests indicate that a particular field needs
900
pounds of phosphoric acid,
750
pounds of nitrogen, and
700
pounds of potash. How many barrels of each type of food should the farmer mix together to supply the necessary nutrients for the field?
6. [10 marks]
Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of
T.
(a) How many vertices does BL(T) have?
(b) How many edges does BL(T) have?
Prove that your answers are correct.
4. [10 marks]
Find both a matching of maximum size and a vertex cover of minimum size in
the following bipartite graph. Prove that your answer is correct.
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5. [10 marks]
Let G = (V,E) be a graph, and let X C V be a set of vertices. Prove that if
|S||N(S)\X for every SCX, then G contains a matching M that matches every
vertex of X (i.e., such that every x X is an end of an edge in M).
Chapter 4 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Intro Stats, Books a la Carte Edition (5th Edition)
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