POP QUIZ –
Thursday, September 15, 2016
Open Book
Chapter 1 Review:
1. A production
process requires a fixed cost of $50,000. The variable cost per unit is $25 and
the revenue per unit is projected to be $45. Write a mathematical expression
for total cost.
2. A production
process requires a fixed cost of $50,000. The variable cost per unit is $25 and
the revenue per unit is projected to be $45. Write a mathematical expression
for total profit.
3. A production
process requires a fixed cost of $50,000. The variable cost per unit is $25 and
the revenue per unit is projected to be $45.
Find the break-even point.
Chapter 2 Review:
4. A farmer decided
to make his own chicken feed by combining alfalfa and corn in large quantities.
Corn costs $400 per batch and alfalfa costs $200 per batch. The farmer’s
chickens have a minimum daily requirement of vitamin K (500 milligrams) and
iron (400 milligrams), but it doesn’t matter whether those elements come from
corn, alfalfa, or some other grain. A unit of corn contains 150 milligrams of
vitamin K and 75 milligrams of iron. A unit of alfalfa contains 250 milligrams
of vitamin K and 50 milligrams of iron. Formulate the linear programming model
for this situation.
Chapter 3 Review:
5. The production
manager for the Whoppy soft drink company is considering the production of two
kinds of soft drinks: regular (R) and diet (D). The company operates one 8-hour
shift per day. Therefore, the production time is 480 minutes per day. During
the production process, one of the main ingredients, syrup, is limited to
maximum production capacity of 675 gallons per day. Production of a regular
case requires 2 minutes and 5 gallons of syrup, while production of a diet case
needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are
$3.00 per case and profits for diet soft drink are $2.00 per case.
The formulation for this problem is
given below.
MAX Z = $3R + $2D
Subject to:
2R
+ 4D ? 480
5R
+ 3D ? 675
The sensitivity report is given below.
Adjustable Cells
|
|
|
Final |
Reduced |
Objective |
Allowable |
Allowable |
|
|
Cell |
Name |
Value |
Cost |
Coefficient |
Increase |
Decrease |
|
|
$B$6 |
Regular = |
90.00 |
0.00 |
3 |
0.33 |
2 |
|
|
$C$6 |
Diet = |
75.00 |
0.00 |
2 |
4 |
0.2 |
|
Constraints
|
|
|
Final |
Shadow |
Constraint |
Allowable |
Allowable |
|
Cell |
Name |
Value |
Price |
R.H. Side |
Increase |
Decrease |
|
$E$3 |
Production (minutes) |
480.00 |
0.07 |
480 |
420 |
210 |
|
$E$4 |
Syrup (gallons) |
675.00 |
0.57 |
675 |
525 |
315 |
5a) What is the optimal daily profit?
5b)How many cases of regular and how
many cases of diet soft drink should Whoppy produce to maximize daily profit?
5c)What is the sensitivity range for the
per-case profit of a diet soft drink? (P.89)
5d)What is the sensitivity range of the
production time?
5e) if the company decides to increase
the amount of syrup it uses during production of these soft drinks to 990 gal. will the current product mix change? If so, show what is
the impact on profit?
