Assignment on Alyssa Mae Berman Product & Operations Management

Alyssa Mae Berman
Product & Operations Management
HW3
Table 3.1: Regular & Super
Consider the following linear program, which maximizes profit for two products--regular (R)
and super (S):
MAX 50R + 75S
s.t.
1.2 R + 1.6 S ≤ 600 assembly (hours)
0.8 R + 0.5 S ≤ 300 paint (hours)
.16 R + 0.4 S ≤ 100 inspection (hours)
Sensitivity Report:
Cell Name
Final
Value
Reduced
Cost
Objective
Coefficient
Allowable
Increase
Allowable
Decrease
$B$7 Regular = 291.67 0.00 50 70 20
$C$7 Super = 133.33 0.00 75 50 43.75
Cell Name
Final
Value
Shadow
Price
Constraint
R.H. Side
Allowable
Increase
Allowable
Decrease
$E$3 Assembly (hr/unit) 563.33 0.00 600 1E+30 36.67
$E$4 Paint (hr/unit) 300.00 33.33 300 39.29 175
$E$5 Inspect (hr/unit) 100.00 145.83 100 12.94 40
1) The optimal number of regular products to produce is _291.67_, and the optimal number of
super products to produce is _133.33_, for total profits of _24,583.25_.
2) If the company wanted to increase the available hours for one of their constraints (assembly,
painting, or inspection) by two hours, they should increase _Assembly (hr/unit).
3) The profit on the super product could increase by __50__ without affecting the product mix.
4) If downtime reduced the available capacity for painting by 40 hours (from 300 to 260 hours),
profits would be reduced by __1333.3___.
5) A change in the market has increased the profit on the super product by $5. Total profit will
increase by _0.00_.

Table 3.2: Taco Loco
Taco Loco is considering a new addition to their menu. They have test marketed a number of
possibilities and narrowed them down to three new products, X, Y, and Z. Each of these products
is made from a different combination of beef, beans, and cheese, and each product has a price
point. Taco Loco feels they can sell an X for $17, a Y for $13, and a Z for $14. The company's
management science consultant formulates the following linear programming model for
company management.
Max R = 14Z + 13Y + 17X
subject to:
Beef 2Z + 3Y + 4X ≤ 28
Cheese 9Z + 8Y + 11X ≤ 80
Beans 4Z + 4Y + 2X ≤ 68
X,Y,Z ≥ 0
The sensitivity report from the computer model reads as follows:
6) Taco Loco should try to purchase additional _Cheese__, but should not buy more _Beans_.
7) Taco Loco should produce both _Z and Y_ but should not make any __X__.
8) Taco Loco will make the same quantity of X, Y, and Z if the amount of cheese at their
disposal is between _74.67_ pounds and _126_ pounds.
9) For humanitarian reasons, Taco Loco decides they would rather make product X than product
Y. The dollar amount that they can both increase the price of Y and reduce the price of X by to
accomplish this reversal of demand is __0.818 dollars or 81.8 cents___.
10) If Taco Loco reduces the price of the X product by about 82 cents, then their optimal product
mix will contain ____0____ X.
11) The amount in euros that a Parisian manager would be willing to pay for additional
resources is the ___1.45 for cheese and 0.45 for Beef_____

12) The Allowable Increase in an Excel sensitivity report is found under the heading of
___Upper Bound___ in the QM for Windows report.
13) The Shadow Price in an Excel sensitivity report is found under the heading of ____Dual
Value_ in the QM for Windows report.
14) For a maximization problem, assume that a constraint is binding. If the original amount of a
resource is 4 lbs. and the range of feasibility (sensitivity range) for this constraint is from 3 lbs.
to 6 lbs., increasing the amount of this resource by 1 lb. will result in the:
A) same product mix, different total profit.
B) different product mix, same total profit as before.
C) same product mix, same total profit.
D) different product mix, different total profit.
Answer: A) same product mix, different total profit.
15) A plant manager is attempting to determine the production schedule of various products to
maximize profit. Assume that a machine hour constraint is binding. If the original amount of
machine hours available is 200 minutes. and the range of feasibility is from 130 minutes to 300
minutes, providing two additional machine hours will result in:
A) the same product mix, different total profit.
B) a different product mix, same total profit as before.
C) the same product mix, same total profit.
D) a different product mix, different total profit.
Answer: D) a different product mix, different total profit.
Table 3.3 Beer, Etc.
The production manager for Beer Etc. produces two kinds of beer: light (L) and dark (D). Two
resources used to produce beer are malt and wheat. The manager can obtain at most 4800 oz of
malt per week and at most 3200 oz of wheat per week, respectively. Each bottle of light beer
requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of
wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle.
16) If the production manager decides to produce of 400 bottles of light beer and 0 bottles of
dark beer, it will result in slack of:
A) malt only.
B) wheat only.
C) both malt and wheat.
D) neither malt nor wheat.
Answer: B) Wheat only
17) Which of the following is not a feasible solution for the scenario in Table 3.3?
A) 0 L and 0 D
B) 0 L and 400 D
C) 200 L and 300 D
D) 300 L and 200 D