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Name:_____________________________
Discussion TA:______________________
Managerial Economics (ARE) 155
University of California, Davis, Fall 2015
Dr. John H. Constantine
Quiz 2 (40 points: each question is worth 5 points), Monday, November 2, 2015
There are 3 pages for this quiz.
A sandwich shop produces five sandwiches: (i) Tuna, (ii) Tuna and Cheese, (iii) Ham, (iv) Ham and
Cheese, and (v) Cheese. The cost the shop incurs to produce each sandwich is found in “Row 6”. The
Solver printout to solve this LP problem is given below,
The firm’s constraints are found in “Rows 9 to 23”. Also in these rows (9 to 23):



Found in “Columns C to G”, are the aij’s.
Found in “Column J” are the constrained amount.
Found in “Column H” are the amounts of each constraint actually used when producing at the
optimal solution.
The questions that follow can refer to either the Solver printout given right below or to the Sensitivity
analysis found on the following page.
B
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Unit Cost
Constraints/Inputs
Bread (slices)
Tuna (oz.)
Ham (oz.)
Cheese (oz.)
Mayo (oz.)
Mustard (oz.)
Lettuce (oz.)
Tomato (oz.)
Package (unit)
Labor (hrs)
Minimum Total Sandwiches
Min Tuna Sandwiches
Min Tuna and Cheese Sandwiches
Min Ham Sandwiches
Min Ham and Cheese Sandwiches
C
D
E
F
G
Tuna
10
2.42
Tuna/Ch
30
2.12
Ham
10
3.35
Ham/Ch
12
3.02
Cheese
8
2.36
Tuna
2
4
Tuna/Ch
2
3
Ham
2
Ham/Ch
2
Cheese
2
4
1.2
1
0.9
3
1
0.5
0.2
0.25
0.5
1
0.08
1
0.25
0.5
1
0.08
1
1
0.25
0.5
1
0.08
1
0.5
0.2
0.25
0.5
1
0.08
1
1
1
1
4
0.5
0.25
0.5
1
0.08
1
H
I
J
Total Cost
176.42
140
130
76
74
54
4.4
17.5
35
70
5.6
70
10
30
10
12
<
<
<
<
<
<
<
<
<
<
>
>
>
>
>
140
130
100
80
72
8
20
40
72
8
70
10
12
10
12
2
Sensitivity Report:
A
B
C
6 Variable Cells
7
Cell
Name
8
$C$5 Tuna
9
$D$5 Tuna/Ch
10
$E$5 Ham
11
$F$5 Ham/Ch
12
$G$5 Cheese
13
14
15 Constraints
16
Cell
Name
17
$H$9 Bread (slices)
18
$H$10 Tuna (oz.)
19
$H$11 Ham (oz.)
20
$H$12 Cheese (oz.)
21
$H$13 Mayo (oz.)
22
$H$14 Mustard (oz.)
23
$H$15 Lettuce (oz.)
24
$H$16 Tomato (oz.)
25
$H$17 Package (unit)
26
$H$18 Labor (hrs)
27
$H$19 Minimum Total Sandwiches
28
$H$20 Min Tuna Sandwiches
29
$H$21 Min Tuna and Cheese Sandwiches
30
$H$22 Min Ham Sandwiches
31
$H$23 Min Ham and Cheese Sandwiches
32
D
E
F
G
H
Final Reduced Objective Allowable Allowable
Value
Cost
Coefficient Increase Decrease
10
0
2.42
1E+30
0.38
30
0
2.12
0.24
1E+30
10
0
3.35
1E+30
0.99
12
0
3.02
1E+30
0.66
8
0
2.36
0.66
0.24
Final Shadow Constraint Allowable Allowable
Value
Price
R.H. Side
Increase Decrease
140
0
140
1E+30
0
130
-0.08
130
24
6
76
0
100
1E+30
24
74
0
80
1E+30
6
54
0
72
1E+30
18
4.4
0
8
1E+30
3.6
17.5
0
20
1E+30
2.5
35
0
40
1E+30
5
70
0
72
1E+30
2
5.6
0
8
1E+30
2.4
70
2.36
70
0
8
10
0.38
10
13.5
10
30
0
12
18
1E+30
10
0.99
10
6
1.5
12
0.66
12
8
2
(a)
How much ham does a ham sandwich require?
(b)
Suppose the firm’s constraint on producing a minimum number of tuna and cheese sandwiches is
increased from 12 to 13. How will this impact the firm’s total cost? Briefly explain your result.
(c)
After the sandwiches are made, how many labor hours remain? Briefly explain your result.
There are more questions on the following page.
3
Questions are continued here.
(d)
Suppose the unit cost for tuna sandwiches increased by $0.50. (i) How does the optimal solution
change and (ii) what happens to total cost. Briefly explain your result.
(e)
Suppose the unit cost for cheese sandwiches decreased by $0.25. (i) How does the optimal
solution change and (ii) what happens to total cost? Briefly explain your result.
(f)
Suppose the quantity of cheese available decreased to 72 ounces. How will this affect (i) the
optimal solution and (ii) the total cost? Briefly explain your result.
(g)
Suppose the shop produced another five sandwiches (from 70 to 75). What will happen to total
costs? Briefly explain your result.
(h)
Suppose the cost of ham sandwiches and cost of ham and cheese sandwiches both decreased by
$0.35 simultaneously. How will this affect (i) the optimal solution and (ii) the total cost? Briefly
explain your result.
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