# MTH 214

1. Draw at least 4 different nets that would form a cube.

2. Are angles of a triangle considered to be supplementary? Explain your answer.

3. Classify the following as true or false. Give Reasons in support of your answer.

a. Two distinct lines that do not intersect are parallel

b. No square is a rectangle

c. If a plane contains one point of a line, it must contain the whole line.

d. A ray contains no endpoints

4. If the measure of an angle is 23 degree 17'18'', what is the measure of its supplement?

5. If the non-base angle of angle of an isosceles triangle has a measure of 70 degree, what is the measure of each base angle?

6. How many diagonals does a decagon have?

7. Is a rhombus a regular polygon? Explain your answer.

8. For the given figure, find the following:

[Please refer to the attachment for the figure]

a. m(< 1)

b. m(< 2)

c. m(< 3)

d. m(< 4)

e. m(< 5)

9. In the figure, how is the measure of angle 4 related to the sum of the measures of angle 1 and angle 2? Justify your answer.

10. In the following figures, find the measures of the angles marked x and y.

[Please refer to the attachment for the figure]

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#### Solution Summary

The solution is comprised of detailed step-by-step calculation and explanation of the various problems related to Combinatorial Mathematics and Geometry. This solution also provides students with a clear perspective of the underlying mathematical aspects.

Operations Research - Linear Programming

State all the assumptions and show all the work. Define your decision variables clearly. Briefly explain the constraints and objectives functions and define all unit of measure.

During the next three months Airco must meet (on time) the following demands for air conditioners: month 1, 300; month 2, 400; month 3, 500. Air conditioners can be produced in either New York or Los Angeles. It takes 1.5 hours of skilled labor to produce an air conditioner in Los Angeles, and 2 hours in New York. It costs $400 to produce an air conditioner in Los Angeles, and $350 in New York. During each month, each city has 429 hours of skilled hour available. It costs $100 to hold an air conditioner inventory for a month. At the beginning of month 1, Airco has 200 air conditioners in stock. Airco wants to know how to minimize the cost of meeting air conditioner demands for the next three months.

a) Mathematically define all decision variables, parameters, constraints, and objective function necessary for formulating the LP model whose solution will tell Airco how it can achieve its objective.

b) Write the LP in standard format.

c) Using the favorite software find the optimal values of the decision variables.