LINEAR PROGRAMMING

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped.  The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg. 
What are the constraints?

• x≤10, y≤3, x+y≤12
• 0≤x≤10, 0≤y≤3, x+y≤12
• x≥0, y≥0, 10x+3y≤12
• x≤10, y≤3, 10x+3y≤12

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with barley can be modeled by P=4000x+3000y . If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

• x≥0

  y≥0

  x+y≥6

  3x+2y≥15

• x≥0

  y≥0

  x+y≤6

  2x+3y≤15

• x≥0

  y≥0

  4000x+y≤6

  2x+600y≤15

• P=4000x+3000y

Solve the system of inequalities. The feasible region is shown by the darkest blue shading.

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x + 3 ≤ 4y

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Trees in urban areas help keep air fresh by absorbing carbon dioxide. A city has RM2100 to spend on planting spruce and maple trees. The land available for planting is 45,000 square feet. Plant a spruce costs RM30 and plant a maple tree costs RM40. A spruce requires an area of 600 square feet and a maple tree requires an area of 900 square feet. A spruce absorbs 650 pounds of carbon dioxide per year and a maple tree absorbs 300 pounds of carbon dioxide per year. (Let x the spruce and y the maple tree). Write and objective function and constraints for a linear program that models the situation. Simplify the inequalities.

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If the given inequality is greater than or greater than or equal, the region _______________ the straight line ax+by+c=0 has to be shaded.

• below

• above

To find the optimal solution for maximum cases, all entries in the objective row of the final tableau are ___________

• positive

• negative

2x + 9 ≥ 3y

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A manufacturing company makes two types of television sets; one is black and white (x) and the other is colour (y). The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a black and white set and Rs 2700 to make a coloured set. The company can spend not more than Rs 648000 a week to make television sets. Constraints are

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