Quantitative Business Analysis: Homework Assignment Solutions

This assignment provides solutions to a series of quantitative business analysis problems. The solutions cover topics such as optimal solutions, sensitivity analysis, linear programming, and break-even analysis. The document includes detailed explanations and calculations for each problem, including the use of graphical representations and algebraic equations. Specific problems addressed involve maximizing profit, determining the optimal number of units to produce, and identifying break-even points. The solutions also analyze the impact of changes in variables, such as selling prices and production costs, on the overall financial outcomes. The assignment aims to help students understand and apply quantitative techniques to solve real-world business challenges, providing a comprehensive guide for understanding the key concepts.

Quantitative Business Analysis
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Problem 7.28
(a) Optimal solution change
Maximize profit=$ 3 X + $ 2Y
Subject to constraints
2 X +Y ≤150
2 X +3 Y ≤300
Graph
Intersection point D
2 X +Y ≤150
2 X +3 Y ≤300
X =37.5 ,Y =75 (Optimal solution)
Maximum (37.5, 75) = 3 *37.5 + 2*75 = 262.5 (Optimal solution)
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When profit per unit of changes to $4.50
Maximum profit = $4.5 X + $2 Y
In this case, the slope of iso-profit line would change.
Maximum (75,0) = 4.5*75 + 2*0 = 337.5(Optimal solution)
(b) Profit per unit Y changes to $3
Maximum profit = $3X + $3Y
Maximum (37.5, 75) = 3 *37.5 +3*75 = 337.5
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Problem 7-29
Optimal solution change
Maximize profit=$ 4 X + $ 6 Y
Subject to constraints
X +2 Y ≤ 8
6 X + 4 Y ≤24
Graph
D: 2 X +4 Y =8∗2=16
6 X + 4 Y =2 4
X =2 ,Y =3
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Maximum value (2,3) = $4*2 + $6*3 =$26 (Optimal solution)
Problem 7 – 18
Linear programming model
Let U is course offered in undergraduate and G is course offered in graduate.
Objective function
Min (Z) = 2500 U + 3000 G
Subject to constraints
Undergraduate: 1U + 0 G >= 30
Graduate: 0 U +1 G > =20
Faculty: U +G > =60
U, G >0 Non negativity constraints.
Solver output
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Answer Report
Sensitivity Report
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Limit Report
Hence, U is course offered in undergraduate and G is course offered in graduate would be
$40 and $20 respectively. Minimum faculty salaries would be $160,000.
Problem 1-14
(a) Total variable cost =?
Total revenue = 20*15 =$300
Total variable cost = 20*8 =$160
(b) Number of shirts and revenue at break-even =?
Break−even units= 350
15−8 =50 units
Break−even revenue=50∗15=$ 750
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Problem 1-15
Variable cost = $20
Selling price = $50
Cost to rent a booth at the fair = $150
Number of units must Ray sell to break-even =?
At break-even
Cost = Revenue
150 + 20 C = 50 C
C = 5
Hence, 5 units must Ray sell to break-even.
Problem 1-16
Variable cost of production = $15 per unit
Break-even point =?
Cost of producing y handcrafted yards then,
Cost of making y handcrafted yards = 15 y + 150
Revenue from y handcrafted yards = 50 y
At break-even
15 y + 150 = 50 y
35 y = 150
Y = 4.29
Break-even point would be 5.
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Problem 1-17
Number of units to sell at break-even (x) =?
Now,
(400 + 3x) + 1000 = 5x
1400 + 3x = 5x
1400 =5x-3x
1400 = 2x
X = 700
Therefore, the number of units to sell programs at break-even would be 700.
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