Operations Research Answers

A. Describe apportionment.
B. What are the different methods of apportionment? Describe each method.
C. Define Huntington-Hill Number.

A. Describe apportionment.
B. What are the different methods of apportionment? Describe each method.
C. Define Huntington-Hill Number.
D. What is Voting?
E. What are the different voting methods used to determine the winner among candidates or options? Describe each method.
F. What are the four basic criteria of fairness? Describe each criterion.

What role is played by mathematics in the following areas?
Economics
Psychology
Music
Data Science

Mr. Trenga plans to start a new business called River Explorers, which will rent canoes and kayaks
to people to travel 10 miles down the Clarion River in Cook Forest State Park. He has $45,000 to
purchase new boats. He can buy the canoes for $600 each and the kayaks for $750 each. His facility
can hold up to 65 boats. The canoes will rent for $25 a day, and the kayaks will rent for $30 a day. How
many canoes and how many kayaks should he buy to earn the most revenue? What is the maximum
revenue

Please solve the following. Create a picture using Desmos.
Find the Min and Max of Z = 5x + 3y
subject to:
4x + 5y ≤ 200
3x + 6y ≤ 180
x ≥ 0; y ≥ 0

A business executive has the option to invest money in two plans: Plan A guarantees that each peso invested will earn PhP0.70 a year later, and plan B guarantees that each peso invested will earn PhP2 after two years. In plan A, investments can be made annually, and in plan B, investments are allowed for periods that are multiples of two years only.

Formulate the LP model in order for the executive to determine how to invest his PhP1,000,000 to maximize the earnings at the end of four years. (CLUE: How much should you invest in plan A and plan B at the start of years 1, 2, 3, and 4?)
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The challenge in this problem is that the return (interest) of plan A and plan B occur in different time periods: plan A’s interest is recognized annually (every year) while plan B’s interest is recognized only every two years.

A health food manufacturer makes two types of protein shakes, Whey and Vegan. Each mixture
contains vitamins, protein, and carbohydrates, in the following proportions:
Carbohydrates (g) Protein (g) Vitamin (g)
Whey 100 400 300
Vegan 200 300 100
Minimum dietary requirements are that a protein shake contain at least 0.9kg of vitamins, 2.2kg of
protein, and 0.8kg of carbohydrate. Whey costs N$20 per kilogram to produce, and Vegan costs
$12.50 per kilogram to produce. Find the number of kilograms of each protein shake that should be
produced to minimize cost.

A health food manufacturer makes two types of protein shakes, Whey and Vegan. Each mixture
contains vitamins, protein, and carbohydrates, in the following proportions:
Carbohydrates (g) Protein (g) Vitamin (g)
Whey 100 400 300
Vegan 200 300 100
Minimum dietary requirements are that a protein shake contain at least 0.9kg of vitamins, 2.2kg of
protein, and 0.8kg of carbohydrate. Whey costs N$20 per kilogram to produce, and Vegan costs
$12.50 per kilogram to produce. Find the number of kilograms of each protein shake that should be
produced to minimize cost.