Math for Modelers
Questions and
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Real exam …..latest update
1. Joanne sells silk-screened t-shirts at a community festival. Her Marginal cost to produce one t-shirt is
$3.50. Her total cost to produce 60 t-shirts is $300, and she sells them for $7 each. Use Python to
graph this information and determine the number of t-shirts Joanne must produce and sell to break
even.
So the equation to solve is
7x = 3.5x + 90
Solve for x to find the breakeven number of shirts:
3.5x = 90 x
= 25.7
At least 26 shirts should be produced
Python Graph:
, (25.7, 180)
Python Code:
# import the matplotlib module
import matplotlib.pyplot from
matplotlib.pyplot import * #
import the numpy module
import numpy # import
linspace
from numpy import linspace
# assign the variables x=
linspace(0,50,100)
y= 3.5*x + 90 z=
7*x
# bring in the chart
figure() # plot the y
equation
, plot(x,y)
# plot the z equation
plot(x,z) # add
legend
legend (('cost','revenue'),loc=2)
# add chart title
title('Breakeven Analysis T-Shirts')
# show chart show()
2. A Rent-A-Truck company plans to spend $14 million on 280 new vehicles. Each commercial van will
cost $55,000, each small truck $20,000, and each large truck $70,000. Past experience shows that
they will need twice as many vans as small trucks. How many of each vehicle can they buy?
Variables
V = vans, S = small truck, L = large truck
New vehicle totals: V + S + L = 280
Spend: 55,000V + 20,000S + 70,000L = 14,000,000
Twice as many vans: V = 2S
Equations in proper form:
V + S + L = 280
55,000V + 20,000S + 70,000L = 14,000,000
V – 2S = 0
Insert into Matrix and reduce using Echelon:
V S L Z
1 1
55,000 20,000 70,000 14,000,000
[ 11 −2 0 2800
]
R2 = R1 (-55,000) + R2
R3 = R1 (-1) + R3
Questions and
Answers 100%
Pass
Real exam …..latest update
1. Joanne sells silk-screened t-shirts at a community festival. Her Marginal cost to produce one t-shirt is
$3.50. Her total cost to produce 60 t-shirts is $300, and she sells them for $7 each. Use Python to
graph this information and determine the number of t-shirts Joanne must produce and sell to break
even.
So the equation to solve is
7x = 3.5x + 90
Solve for x to find the breakeven number of shirts:
3.5x = 90 x
= 25.7
At least 26 shirts should be produced
Python Graph:
, (25.7, 180)
Python Code:
# import the matplotlib module
import matplotlib.pyplot from
matplotlib.pyplot import * #
import the numpy module
import numpy # import
linspace
from numpy import linspace
# assign the variables x=
linspace(0,50,100)
y= 3.5*x + 90 z=
7*x
# bring in the chart
figure() # plot the y
equation
, plot(x,y)
# plot the z equation
plot(x,z) # add
legend
legend (('cost','revenue'),loc=2)
# add chart title
title('Breakeven Analysis T-Shirts')
# show chart show()
2. A Rent-A-Truck company plans to spend $14 million on 280 new vehicles. Each commercial van will
cost $55,000, each small truck $20,000, and each large truck $70,000. Past experience shows that
they will need twice as many vans as small trucks. How many of each vehicle can they buy?
Variables
V = vans, S = small truck, L = large truck
New vehicle totals: V + S + L = 280
Spend: 55,000V + 20,000S + 70,000L = 14,000,000
Twice as many vans: V = 2S
Equations in proper form:
V + S + L = 280
55,000V + 20,000S + 70,000L = 14,000,000
V – 2S = 0
Insert into Matrix and reduce using Echelon:
V S L Z
1 1
55,000 20,000 70,000 14,000,000
[ 11 −2 0 2800
]
R2 = R1 (-55,000) + R2
R3 = R1 (-1) + R3
