Exam 9: Linear Programming

The equation 3xy = 9 is linear.

What combination of x and y will yield the optimum solution for this problem? Maximize Z = $3x + $15y; Subject to: (1)2x + 4y $\le$ 12 (2)5x + 2y $\le$ 10

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.Which of the following is not a feasible production combination?

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.What is the objective function?

A company produces two products (A and B)using three resources (I,II,and III).Each product A requires 1 unit of resource I and 3 units of resource II; and has a profit of $1.Each product B requires 2 units of resource I,3 units of resource II,and 4 units of resource III; and has a profit of $3.Resource I is constrained to 40 units maximum per day; resource II,90 units; and resource III,60 units.Is the production combination 15 A's and 15 B's feasible?

When a change in the value of an objective function coefficient remains within the range of optimality,the optimal solution would also remain the same.

An example of a decision variable in an LP problem is profit maximization.

An objective function represents a family of parallel lines.

What is the linear programming approach where substituting the coordinates of each corner point into the objective function determines the corner point which is optimal?

A company produces two products (A and B)using three resources (I,II,and III).Each product A requires 1 unit of resource I and 3 units of resource II; and has a profit of $1.Each product B requires 2 units of resource I,3 units of resource II,and 4 units of resource III; and has a profit of $3.Resource I is constrained to 40 units maximum per day; resource II,90 units; and resource III,60 units.Is the production combination 10 A's and 10 B's feasible?

The production planner for a private label soft drink maker is planning the production of two soft drinks: root beer (R)and sassafras soda (S).Two resources are constrained: production time (T),of which she has at most 12 hours per day; and carbonated water (W),of which she can get at most 1500 gallons per day.A case of root beer requires 2 minutes of time and 5 gallons of water to produce,while a case of sassafras soda requires 3 minutes of time and 5 gallons of water.Profits for the root beer are $6.00 per case,and profits for the sassafras soda are $4.00 per case.What is the production time constraint (in minutes)?

An electronics firm produces two models of pocket calculators: the A-100 (A),which is an inexpensive four-function calculator,and the B-200 (B),which also features square root and percent functions.Each model uses one (the same)circuit board,of which there are only 2,500 available for this week's production.Also,the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators,of which the A-100 requires 15 minutes (.25 hours)each,and the B-200 requires 30 minutes (.5 hours)each to produce.The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's.Profits for the A-100 are $1.00 each,and profits for the B-200 are $4.00 each.What are optimal weekly profits?

For a nonbinding constraint,if the left side is greater than the right side,we say that there is surplus; if the left side is smaller than the right side,we say that there is slack.

The logistics/operations manager of a mail order house purchases two products for resale: King Beds (K)and Queen Beds (Q).Each King Bed costs $500 and requires 100 cubic feet of storage space,and each Queen Bed costs $300 and requires 90 cubic feet of storage space.The manager has $75,000 to invest in beds this week,and her warehouse has 18,000 cubic feet available for storage.Profit for each King Bed is $300,and for each Queen Bed is $150.What is the maximum profit?

The owner of Crackers,Inc.produces two kinds of crackers: Deluxe (D)and Classic (C).She has a limited amount of the three ingredients used to produce these crackers available for her next production run: 4,800 ounces of sugar; 9,600 ounces of flour,and 2,000 ounces of salt.A box of Deluxe crackers requires 2 ounces of sugar,6 ounces of flour,and 1 ounce of salt to produce; while a box of Classic crackers requires 3 ounces of sugar,8 ounces of flour,and 2 ounces of salt.Profits for a box of Deluxe crackers are $0.40; and for a box of Classic crackers,$0.50.Which of the following is not a feasible production combination?

The theoretical limit on the number of decision variables that can be handled by the simplex method in a single problem is:

The operations manager for the Blue Moon Brewing Co.produces two beers: Lite (L)and Dark (D).Two of his resources are constrained: production time,which is limited to 8 hours (480 minutes)per day; and malt extract (one of his ingredients),of which he can get only 675 gallons each day.To produce a keg of Lite beer requires 2 minutes of time and 5 gallons of malt extract,while each keg of Dark beer needs 4 minutes of time and 3 gallons of malt extract.Profits for Lite beer are $3.00 per keg,and profits for Dark beer are $2.00 per keg.What is the time constraint?

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Colombia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.What is the Colombian bean constraint?

The production planner for Fine Coffees,Inc.produces two coffee blends: American (A)and British (B).Two of his resources are constrained: Columbia beans,of which he can get at most 300 pounds (4,800 ounces)per week; and Dominican beans,of which he can get at most 200 pounds (3,200 ounces)per week.Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans; while a pound of British blend coffee uses 8 ounces of each type of bean.Profits for the American blend are $2.00 per pound,and profits for the British blend are $1.00 per pound.What is the objective function?

The simplex method is an LP algorithm that can solve problems having more than two decision variables.