MATH 8 Final Exam

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Industrial Engineering

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Oct 30, 2023

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NAME:____________________________ Final Exam Show all work! 1. Using the Simplex method Maximize 𝑧 = 2𝑥 1 + 𝑥 2 + 𝑥 3 subject to the constraints { 4𝑥 1 + 12𝑥 2 + 𝑥 3 ≤ 124 8𝑥 1 + 5𝑥 3 ≤ 152 𝑥 1 ≥ 0, 𝑥 2 ≥ 0, 𝑥 3 ≥ 0

2. Solve by solving the dual problem. Minimize 𝑧 = 42𝑥 1 + 70𝑥 2 subject to { 5𝑥 1 + 4𝑥 2 ≥ 30 3𝑥 1 + 4𝑥 2 ≥ 22 𝑥 1 ≥ 0, 𝑥 2 ≥ 0

3. Using the Simplex method Maximize 𝑧 = 𝑥 1 − 2𝑥 2 subject to { 𝑥 1 + 𝑥 2 ≥ 10 2𝑥 1 + 5𝑥 2 ≤ 60 𝑥 1 ≥ 0, 𝑥 2 ≥ 0

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4. Using the Simplex method Maximize 𝑧 = 𝑥 1 + 4𝑥 2 Subject to { −4𝑥 1 + 𝑥 2 ≤ 2 2𝑥 1 − 𝑥 2 ≤ 1 𝑥 1 ≥ 0, 𝑥 2 ≥ 0

5. Sophie G. Inc. makes three types of bicycle frames: cruiser, road, and mountain bike. Each frame requires units of aluminum tubing and units of steel tubing as shown in the table below. Cruiser Road Mountain Aluminum 5 12 4 Steel 17 10 30 The company has available 2000 units of aluminum tubing per week and 9000 units of steel tubing per week. The company makes $40 profit on each cruiser frame, $60 profit on each road frame and $40 profit on each mountain bike frame. How many of each type should the company make in order to maximize weekly profits? (round your answers to the nearest whole frame).

6. The city of Hewitt sold $365,000 in bonds to build a new city park. The interest rate is 7.2% and is to be paid annually for 4 years. Find the annual interest and the total interest. 7. Jim McAtee bought a 1928 Model A Ford for $8250 and sold it 2 years later for $9300. Find the annual compound rate of return earned on his investment.

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8. Anthony decides to help his new niece attend a private college in 18 years. The projected cost of tuition, fees, and room and board when she starts amounts to $65,000 per year. How much should Anthony invest each year for the next 18 years to pay for the first-year costs? Assume 5.5% interest compounded annually. 9. The national interest rate for a 30 year home loan in 2021 was around 3% and the average cost of a home in Redding CA was $313,162. a. What is the monthly payment (before factoring in fees, insurance, taxes, etc.) assuming the 3% interest rate on a $313,162 house over a 30 year loan compounding monthly? b. How much has the loan cost at the end of 30 years.