Break-even analysis. A small plant manufactures riding lawn mowers. The plant has fixed costs (leases, insurance, etc.) of $ 48 , 000 per day and variable costs (labor, materials, etc.) of $ 48 , 000 per unit produced. The mowers are sold for $ 1 , 800 each. So the cost and revenue equations are y = 48 , 000 + 1 , 400 x Cost equation y = 1 , 800 x Revenue equation where x is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars. (A) How many units must be manufactured and sold each day for the company to break even? (B) Graph both equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.
Break-even analysis. A small plant manufactures riding lawn mowers. The plant has fixed costs (leases, insurance, etc.) of $ 48 , 000 per day and variable costs (labor, materials, etc.) of $ 48 , 000 per unit produced. The mowers are sold for $ 1 , 800 each. So the cost and revenue equations are y = 48 , 000 + 1 , 400 x Cost equation y = 1 , 800 x Revenue equation where x is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars. (A) How many units must be manufactured and sold each day for the company to break even? (B) Graph both equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.
Solution Summary: The author calculates the number of units the company manufactured and sold each day for break-even. The cost equation and the revenue equation are on the same coordinate system.
Break-even analysis. A small plant manufactures riding lawn mowers. The plant has fixed costs (leases, insurance, etc.) of
$
48
,
000
per day and variable costs (labor, materials, etc.) of
$
48
,
000
per unit produced. The mowers are sold for
$
1
,
800
each. So the cost and revenue equations are
y
=
48
,
000
+
1
,
400
x
Cost
equation
y
=
1
,
800
x
Revenue equation
where
x
is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars.
(A) How many units must be manufactured and sold each day for the company to break even?
(B) Graph both equations in the same coordinate system and show the break-even point. Interpret the regions between the lines to the left and to the right of the break-even point.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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.
ย
ພ
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
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