Math Exam Final Review Worksheet With Answer Key - M118, Indiana University Southeast Page 4
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1238) A trucking firm wants to purchase 10 trucks that will provide exactly 28 tons of additional shipping capacity.
A model A truck holds 2 tons, a model B truck holds 3 tons, and a model C truck holds 5 tons. How many
trucks of each model should the company purchase to provide the additional shipping capacity? Set up a
system of linear equations and solve using Gauss-Jordan elimination.
39) Find the coordinates of the corner points of the solution region for:
3x + 4y ≥ 36
3x + y ≤ 18
x ≥ 0
y ≥ 0
40) A retail company offers, through two different stores in a city, three models, A, B, and C, of a particular brand
of camping stove. The inventory of each model on hand in each store is summarized in matrix M. Wholesale
(W) and retail (R) prices of each model are summarized in matrix N. Find the product MN and label its
columns and rows appropriately. What is the wholesale value of the inventory in Store 1?
A B C
W R
60 90
M = 2 0 1
N =
120 150
3 3 0
40 50
41) Formulate the following problem as a linear programming problem (DO NOT SOLVE).
A company which produces three kinds of spaghetti sauce has two plants. The East plant produces 3,500 jars
of plain sauce, 6,500 jars of sauce with mushrooms, and 3,000 jars of hot spicy sauce per day. The West plant
produces 2,500 jars of plain sauce, 2,000 jars of sauce with mushrooms, and 1,500 jars of hot spicy sauce per
day. The cost to operate the East plant is $8,500 per day and the cost to operate the West plant is $9,500 per
day. How many days should each plant operate to minimize cost and to fill an order for at least 8,000 jars of
plain sauce, 9,000 jars of sauce with mushrooms, and 6,000 jars of hot spicy sauce? (Let x 1 equal the number of
days East plant should operate and x 2 equal the number of days West plant should operate.)
1 1
42) This message was encoded with the following matrix:
2 3
Decode this message:
28 64 32 91 30 65 24 60 38 99 42 99 35 82 36 81 46 119 13 31 23 51.
43) A vineyard produces two special wines, a white and a red. A bottle of the white wine requires 14 pounds of
grapes and 1 hour of processing time. A bottle of red wine requires 25 pounds of grapes and 2 hours of
processing time. The vineyard has on had 2,198 pounds of grapes and can allot 160 hours of processing time
to the productions of these wines. A bottle of the white wine sells for $11.00, while a bottle of the red wine
sells for $20.00. How many bottles of each type should the vineyard produce in order to maximize gross sales?
(Solve using the geometric method.)
44) Solve the following linear programming problem by determining the feasible region on the graph and testing
the corner points.
Maximize: P = 4x 1 + 3x 2
Subject to: 3x 1 + 2x 2 ≤ 30
4x 1 + x 2 ≤ 20
x 1 , x 2 ≥ 0
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