Problem Set 2 : Equations and Inequalities with Two Variables
4:48 AM
Muhammad Yusuf
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1. Maximize:
P = 3x + 4y
Subject to:
2x + y ≤ 6
x + y ≤ 4
x ≥ 0
y ≥ 0
2. Minimize:
C = 2x - 3y
Subject to:
4x + 5y ≤ 40
2x - y ≥ 0
x ≤ 6
x ≥ 0
y ≥ 0
3. A tailor has 80 square metres of cotton material and 120 square metres of wool. A suit requires 1 square metre of cotton and 3 square metres of wool. A dress requires 2 square metre of cotton and 1 square metre of wool. How many of each should the tailor make to maximize revenue, if a suit sells for $110 and a dress sells for $80?
4. A company makes two types of calculators, Calculator A and Calculator B. Each calculator must be tested after it is assembled. The amount of time required for assembling Calculator A is 4 hours and the amount of time required for assembling Calculator B is also 4 hours. The amount of time for testing Calculator A is 2.5 hours, and the amount of time for testing Calculator B is 1.5 hours. Each week there are 104 working hours for assembling and 60 working hours for testing. If the company makes a profit of $4 on each Calculator A and $2.50 on each Calculator B, how many of each should it produce to maximize its weekly profits?
5. Minimize:
C = x - 4y
Subject to:
2x + 3y ≥ 6
x ≤ 8
y ≤ 12
x ≥ 0
y ≥ 0
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