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four companies viz. W,X,Y, and Z supply the requirements of three warehouse viz. A, B, and C respectively. the companies availability, warehouse requirements and the unit cost of transporatation are given in the following table. find an initial basic feasible solution using
Discuss five strands of Mathematical proficiency and name different aspects of learning mathematics that each covers
A. What is weighted voting system?

B. What are the different types of weighted voting?

C. Describe Banzhaf Power Index.
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

Q2) A trucking company has a contract to move 115 truckloads of sand per week between three sand-washing plants W,X and Y, and three destinations, A,B and C. Cost and volume information is given below.

Compute the optimal transportation cost using:

(a) Northwest corner method.

(b) Least-Cost method.

(c) Vogel’s approximation method.


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 hardware store packages handyman bags of screws, bolts, nuts, and washers. Screws come in 100-lb boxes and cost $110 each, bolts come in 100-lb boxes and cost $150 each, nuts come in 80-lb boxes and cost $70 each, and washers come in 30-lb boxes and cost $20 each. The handyman package weighs at least 1 lb and must include, by weight, at least 10% screws and 25% bolts, and at most 15% nuts and 10% washers. To balance the package, the number bolts cannot exceed the number of nuts or the number of washers. A bolt weights 10 times as much as a nut and 50 times as much as a washer.

Formulate the LP model to determine the optimal mix of the package.
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