Q1. Bob, a new manufacturer, has determined that his fixed monthly costs amount to $60,000, and his variable costs amount to $15 Based on marketing research, he wishes to sell his product at a selling price of $45.
Part 1- Determine his break-even point.
Part 2- Because of new competition, Bob can only sell his product for $36, what effect will this new selling price have on his break-even point?
Part 3- Bob is attempting to reduce his variable costs. If his fixed costs remains at $60,000, and his selling price is $36, what would his variable costs need to be in achieve the break-even point determined in Part 1?
Q2. The following payoff matrix gives the strategies and payoffs for Player A and Player B.
Determine the percentage of time Player A should play the A1 strategy.
Determine the value of the game.
Q3. The following payoff matrix gives the strategies and payoffs for Player A and Player B.
Part 1: Determine the percentage of time Player A should play the A1 strategy.
Part 2: Determine the percentage of time Player B should play the B2 strategy.
Part 3: What is the value of the game?
Part 4: Which player has the advantage?
Q4. Consider the following payoff table
|
|
Market Condition
|
|
Stock
|
Poor
|
Average
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Good
|
Excellent
|
|
Alpha
|
50
|
75
|
20
|
30
|
|
Beta
|
80
|
15
|
40
|
50
|
|
Gamma
|
-100
|
300
|
-50
|
10
|
|
Delta
|
25
|
25
|
25
|
25
|
|
Probabilities
|
0.5
|
0.1
|
0.35
|
0.05
|
Under the maximin criterion, which stock would you buy?
Under the Equally Likely criterion, which stock would you buy?
Under minimax regret, which stock would you buy?
Under the maximax criterion, which stock would you buy?
Under the criterion of realism, with α = 0.6, which stock would you buy?
Using the probabilities provided, which stock would you buy?
What is the EMV of your stock choice?
Q5. A manufacturing company produces two milk-based drinks: Fully and Litey. Each Fully bottle sold earns a profit of $2 and each Litey bottle earns a profit of $1. Milk and sugar are two main ingredients for the products. Each week, 4800 oz of milk are available, and 3600 oz of sugar are available. Each bottle of Fully requires 10 oz of milk and 8 oz of sugar. Each bottle of Litey requires 8 oz of milk and 4 oz of sugar.
Which of the following is NOT a corner point on the feasible region?
Which is the optimal solution?
What is the value of the optimal solution?
Which special case of LP is seen in this problem?
Q6. The formulation of a LP problem is given below:
Let A = Number of Product A manufactured
Let B = Number of Product B manufactured
Let C = Number of Product C manufactured
Let D = Number of Product D manufactured
Max Z = 100A + 120B + 150C + 125D
Subject to: A + 2B+ 2C + 2D ≤ 108 Constraint 1: Space
3A + 5B + D ≤ 120 Constraint 2: Setup time
A + C = ≤25 Constraint 3: Max demand for A&C
B + C + D ≥ 50 Constraint 4: Min demand for B, C
A, B, C, D ≥ 0
The optimal solution and sensitivity are provided below,
Objective Function Value = 7475.000.
|
Variable
|
Value
|
Reduced Cost
|
Original Val
|
Lower Bound
|
Upper Bound
|
|
A
|
8
|
0
|
100
|
87.5
|
Infinity
|
|
B
|
0
|
5
|
120
|
-Infinity
|
125
|
|
C
|
17
|
0
|
150
|
125
|
162.5
|
|
D
|
33
|
0
|
125
|
120
|
150
|
|
Constraint
|
Dual Value
|
Stack/Surplus
|
Original Val
|
Lower Bound
|
Upper Bound
|
|
1-Space
|
75
|
0
|
108
|
100
|
123.75
|
|
2-Setup Time
|
0
|
63
|
120
|
57
|
Infinity
|
|
3-Max demand for A and C
|
25
|
0
|
25
|
8
|
58
|
|
4-Min demand for B, C, D
|
-25
|
0
|
50
|
41.5
|
54
|
The total profit to be realized: Z =
If the company is able to increase the profit per Product A to $150, what will be the objective function value?
If there is a decrease in the profit per unit of Product D from $125 to $120, what will be the objective function value?
If the company is able to produce 25 more units of Product B, by how much will the objective function value change?
If the company is able to hire additional labour to increase the amount of setup time available, how much should the company pay to each additional unit?
You can rent a warehouse in order to obtain additional space, at a cost of $100 per unit. How many units should the company rent?