Notes for math 141
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Section 2.3-2.5
Finite Mathematics
Application of matrix products
Example 1.1. The Yummy Cake Company makes three types of cakes: Angel Food,
Italian Cream, and Chocolate. The company produces its cakes in College Station,
Santa Cruz, and Austin using two main ingredients, sugar and flour.
a) Each kilogram of Angel Food requires 0.1 kg of sugar and 0.5 kg of flour. Each
kilogram of Italian Cream requires 0.6 kg of sugar and 0.2 kg of flour. Each kilogram
of Chocolate requires 0.3 kg of sugar and 0:3 kg of flour. Put this information into a
2 × 3 matrix.
b) The cost of 1 kg of sugar is $1 in College Station, $4 in Santa Cruz and $2 in
Austin. The cost of 1 kg of flour is $0.50 in College Station, $1.50 in Santa Cruz
and $1 in Austin. Put this information into a matrix in such a way that when it is
multiplied by the matrix in part a) it will tell us the cost of producing each kind of
cake in each city. Find the resulting product matrix.
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Notes for math 141
2
Section 2.3-2.5
Finite Mathematics
Linear equations and Quadratic equation
Example 2.1. Find an equation of the line L passing through (1,-1) and (2,5), find
the x-intercept and y-interept.
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Notes for math 141
Section 2.3-2.5
Finite Mathematics
Example 2.2. If the supply equation is 3x-2p+45=0 and the demand equation is
3x+3p-35=0, where x is the quantity demanded in units of 1000 and p is the unit
price in dollars, find the equilibrium demand and equilibrium price.
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Notes for math 141
Section 2.3-2.5
Finite Mathematics
Example 2.3. A company has determined that if the price of an item is $40, then
150 will be demanded by consumers. When the price is $45, then 100 items are
demanded by consumers. (a) Find the price-demand equation, assuming that it is
linear. (b) Find the revenue function. (c) Find the number of items sold that will
give the maximum revenue. What is the maximum revenue? (d) What is the price of
each item when maximum revenue is achieved? (e) If the company has a fixed cost
of $3520 and a variable cost of $12 per item, find the company’s linear cost function.
(f) Find the company’s profit function. (g) Find the number of items sold that will
give the maximum profit. What is the maximum profit? (h) How many items should
be sold for the company to break even?
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Notes for math 141
3
Section 2.3-2.5
Finite Mathematics
Systems of Linear Equations
Example 3.1. Jennifer has made it through her ten year class reunion. She is wanting
to remember how many former classmates, spouses, and former teachers attended the
reunion. She has lost her records but recalls that the ticket sales totaled $4,775. She
charged $30 for each former classmate, $25 for each spouse, and $20 for each former
teacher. She recalls that the number of former classmates and spouses combined
was 130 more than the number of former teachers. She also recalls that there were
five times as many former classmates there as spouses. Help Jennifer remember the
number of former classmates, spouses, and former teachers that attended the reunion.
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Notes for math 141
Section 2.3-2.5
Finite Mathematics
Example 3.2. Solve the following system of equations using Gauss Jordan Elimination by hand:
⎧
⎪
⎪2x − y = 3
⎨
⎪
⎪
⎩6x − y = 11
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Notes for math 141
Section 2.3-2.5
Finite Mathematics
Example 3.3. Solve the following system of equations using Gauss Jordan Elimination.(Also
learn how to pivot a11
⎧
2x − y − 2z = 1
⎪
⎪
⎪
⎪
⎨6x − y − z = 5
⎪
⎪
⎪
⎪
⎩4x + z = 4
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