Business 2400 Assignment 2 Fall,
Question 4
We are given the following algebraic model:
maximize 4x1
subject to
(1) 15x1
(2) 40x1
(3) 10x1
(4) 4x1
+
9x2
+
+
+
+
3x2
10x2
8x2
20x2
x1
,
≤
≥
≤
≤
450
400
420
588
x2 ≥
0
a. Solve the model graphically, using a 50 by 50 grid.
50
x2 40
30
20
10
0
0
10
20
30
40
x1
50
b. Perform a sensitivity analysis for each of the objective function coefficients.
c. Perform a sensitivity analysis for the right-hand-side values for each of the nonbinding constraints.
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d. Find the AI (allowable increase) and AD (allowable decrease) for the righthand- side
values for each of the two binding constraints.
e. For each of the two binding constraints, find the change to each variable as function
of the right-hand side value, and from these relationships calculate the two shadow
prices.
Question 5
A company that makes concrete sells it in three quality levels, type 1 the being lowest, and type
3 being the highest. After deducting all variable costs, the net revenue is $30 per Tonne for type
1, $40 for type 2, and $50 per type 3. There are three operations, each of which limits the amount
of production: crushing, grinding, and mixing. In addition, each type of concrete must be
inspected. The model has been formulated as:
Let X1, X2, and X3 represent respectively the number of type 1, 2, and 3 made in Tonnes per
hour.
maximize 30X1 +
subject to
40X2 +
50X3
Crushing 2X1 +
4X2 +
5X3 ≤
80
Grinding 6X1 +
8X2 + 12X3 ≤ 210
Mixing
5X1 +
7X2 +
8X3 ≤ 146
Inspection 3X1 +
4X2 +
5X3 ≥
50
non-negativity
X1 ,
X2 ,
X3 ≥
0
(a) Solve using a spreadsheet Solver, and print the Answer and Sensitivity Reports.
(b) State the solution in words, and indicate which constraints are binding.
(c) By using the information from the Sensitivity Report (NOT by re-running the model each
time), give the predicted change to the objective function value (and the reasoning behind
your answer) for the following situations (taken one at a time). If the OFV cannot be
predicted exactly, then give an answer such as “the OFV will increase by at least $100”.
(i)
The revenue per Tonne for type 1 concrete rises by $0.70.
(ii) There are three fewer units of crushing.
(iii) The revenue per Tonne for type 2 concrete increases by $8.00.
(iv) The number of units of grinding decreases by 20. (v) The number of units of mixing
increases by nine.
(vi) The price per Tonnes of Type 1 cement falls by $3, and the price for Type 3 concrete
rises by $15.
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