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1.ABCD company is an office equipment company that produces two types of desks:
1.ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold to national chains shops.
Instructions:
Develop a linear optimization model to determine how many of each type of desk the ABCD company should make next week to maximize profit contribution [Assume: S = units of standard desk produced and D = units of deluxe desk produced. No need to solve the model, neither graphically nor by Solver: just develop the mathematical model for this part]
2.ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak tops, more expensive hardware, and require additional time for finishing and polishing. Standard desks require 80 square feet of pine and 10 hours of labor, while deluxe desks require 60 square feet of pine, 18 square feet of oak, and 16 hours of labor. For the next week, the company has 5,000 square feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $150, while deluxe desks net a profit of $320. All desks can be sold to national chains shops.
Instructions:
If the spreadsheet and Excel Solver results are given to you as follows (see Table 1 below), address the following questions:
What are your Binding Constraints?
What is your Optimum profit [hint: maximized profit]?
What are your slack values for Pine, Oak, and Labor?
Looking at the Shadow prices, how much would the objective profit increase by if you were to increase labor hours by 50?
If the optimum solution for standard desk stays the same, but deluxe desk numbers increased, what would be your estimated deluxe desks in this case? Would you recommend this option? Why? Hints: Notice that by increasing labor hours by 50, the S stays as an original optimum solution given in the information of Solver, but D will increase. The question is asking you to find how much the objective profit would go up and what would be the estimated number for D [calculated from your constraints. Decimal number is accepted].
What would be the changes in objective profit $, if we increase the Pine by one unit and the Oak by one unit, i.e., Pine available=5001 and Oak available=751.
What % of available Oak can be reduced without it affecting the current (given) optimum solution?
What % of available Pine can be reduced without affecting the current (given) optimum solution?
How much should the standard desk unit profit of $150 be increased by in order for Standard desks to be produced (i.e. become a positive number)?
Given results after developing the excel LP and Solver:
Excel program
Standard
Deluxe
Availability
Pine
80
60
5000
Oak
0
18
750
Labor
10
16
400
Profit/unit
$150
$320
Number produced
0
25.0
Total (per week)
Profit contribution
$0
$8,000
$8,000
Amount Used
Pine
1500
Oak
450
Labor
400
Solver Sensitivity Report:
Variable Cells
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$21
Number produced Standard
0
-50
150
50
1E+30
$C$21
Number produced Deluxe
25
0
320
1E+30
80
Solver Constraints
Final
Shadow
Constraint
Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$B$25
Pine Amount Used
1500
0
5000
1E+30
3500
$B$26
Oak Amount Used
450
0
750
1E+30
300
$B$27
Labor Amount Used
400
20
400
266.6666667
400
Use a graphical procedure and manual calculation to determine the optimal solution to the following linear program for decision-making purposes. Excel Linear Programing has been used to generate the following graph on the objective and constraints (please notice that you do not need to create this program in Excel, just use the outcomes given here to answer the questions):
Objective: Minimize cost C C= 0.5 Xa + 0.4 Xb Subject to: 2Xa + 5Xb >= 10 3Xa + Xb >= 9 Xb >= 2 Where Xa and Xb are >= 0 Please notice Xa is taken on x-axis and Xb on y-axis Instructions:
Note: Questions should be answered by looking at your objective and constraints and the provided Excel’s graphical results (No Excel program needs to be developed): Identify the feasible region by the areas bounded with the letters. For example, you could identify your feasible solution region as: Area EBJ (just as an example). Hint, you need to test a point in each of the inequalities to determine the solution for each of them, and then decide what will be the final feasible solution region that matches all these inequalities.
Show your optimum corner on the graph, as an example, point H, D, F, or whatever you think the correct optimum corner is. Calculate the coordinates (Xa and Xb) for this optimum point using the intersection of the 2 lines that create this optimum corner (mathematically and exact values, not just guessing from the graph). Hints, there are 2 trial cost lines plotted on the graph [C=1 and C=0.5] to show the direction of minimizing the cost within the feasible region.
What is your minimized cost value for this model
VanMetals has $3500 available for the production of new products. Wall Inc. will buy all the products they can produceAfter an initial screening, VanMetals reduced the production alternatives to tables and chairs. Each table can be produced with a cost of $400. Each chair can be produced for $350.VanMetals can devote up to 100 hours to these new products; each table is expected to require 16 hours, and each chair is expected to require 8 hours. The selling prices are $600 per table and $400 per chair.VanMetals’s owner would like to use all-integer linear programming without relaxation to determine the number of tables and the number of chairs to produce to maximize revenue.
What are the decision variables? (2 points)
What is the objective function for revenue? (3 points)
What are the constraints? (4 points)
What is the number of tables and the number of chairs to be produced to maximize revenue? (4 points)
What is the Maximum revenue they can expect? (3 points)
Draw the graphical solution of the all-integer problem. (4 points)
take a picture of all your work and upload the files. (You can use Excel Solver)
=====================================================TM and Mayota are the only companies serving a market. TM can introduce a new line of vehicles to the market. In response Mayota can introduce a new line of vehicles as well. They both know their competitive advantages and each sale of one will reduce the market share of the other.
The table below shows the expected gain in market share for TM thousands of units
Mayota
SedanSUVVanSportCoup
TMSedan123-24
SUV03-143
Van22123
Sport22343
Coup01432
What is the best strategy for TM? (2 points)
What is the best strategy for Mayota? (2 points)
If TM decides to produce SUV, what will be the best choice of production for Mayota? (2 points)
If Mayota decides to produce SUV, what will be the best choice of production for TM? (2 points)
Does this game have a pure strategy? (2 points)
Show you calculations and upload 6. Expected value Applied to Business ApplicationABCD Manufacturing Company (ABCD) has developed a new product.The functionality and feasibility of the product has been proven, but each sale will require significant customer support. ABCD must make a decision regarding the level of sales and dedicated to this product. Finally, a complete division (d1~ 4) consisting of about twelve people may be created to fully automate the product and engage in an extensive marketing campaign.The potential profit from each decision alternative depends on the market acceptance or demand for this product which may be high, moderate, or low. If market acceptance is high, each of the four decision alternatives, d1 through d4, will yield a profit of -200, 0, 300, and 900 thousand dollars respectively. If there is a moderate demand, the profits are likely to be 100, 100, 200, and -200 thousand dollars respectively. If the demand turns out to be low, then the profits will be 200, 150, -200, and -500 thousand dollars respectively.The industry experience with such products provides a probability estimate of demand to be high, moderate, and low as 0.3, 0.5, and 0.2 respectively. Which of the four decision alternatives should be selected by ABCD? What will be the expected profit from this decision? If a market research firm can provide perfect information about demand to ABCD (i.e., whether it will be high, moderate, or low) before a product launch decision is made, how much is that information worth to ABCD?
Hints: To structure this decision-making problem, we begin by constructing a payoff table. Our payoff table will, therefore, have 4 rows and 3 columns. The numbers inside the payoff table will represent the profit we will make for each combination of demand and decision alternative. Demand of Events/Decision AlternativeLowModerateHigh
D1
D2
D3
D4
Hint: Probability of each event: The most common approach to solve such decision-making problems with known probabilities is to use the expected value approach.
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