Exam 9: Linear Programming

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.For the production combination of 800 boxes of Deluxe and 600 boxes of Classic,which resource is slack (not fully used)?

In the graphical solution method for minimization problems,we find the optimal corner point by sliding the objective function line (which is an isocost line)toward the origin instead of away from it.

The removal of a redundant constraint does not affect the feasible solution space.

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 are optimal daily profits?

For the constraints given below,which point is in the feasible solution space of this minimization problem? (1)14x + 6y > 42 (2)x + 3y > 6

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.What is the objective function?

A constraint that does not form a unique boundary of the feasible solution space is a:

Which of the following is not a component of the structure of a linear programming model?

A small firm makes three products,which all follow the same three step process,which consists of milling,inspection,and drilling.Product A requires 6 minutes of milling,5 minutes of inspection,and 4 minutes of drilling; product B requires 2.5 minutes of milling,2 minutes of inspection,and 2 minutes of drilling; and product C requires 5 minutes of milling,4 minutes of inspection,and 8 minutes of drilling.The department has 20 hours available during the next period for milling,15 hours for inspection,and 24 hours for drilling.Product A contributes $6.00 per unit to profit,product B contributes $4.00 per unit,and product C contributes $10.00 per unit.Determine the optimum mix of products in terms of maximizing contributions to profits for the next period.

The equation 5x + 7y = 10 is linear.

The term "isoprofit" line means that all points on the line will yield the same profit.

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.For the purchase combination 0 King Beds and 200 Queen Beds,which resource is "slack" (not fully used)?

A maximization problem may be characterized by all greater than or equal to constraints.

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 objective function?

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 is the assembly time constraint (in hours)?

The logical approach,from beginning to end,for assembling a linear programming model begins with:

For the constraints given below,which point is in the feasible solution space of this maximization problem? (1)14x + 6y $\le$ 42 (2)x - y $\le$ 3

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.What are the corner points of the feasible solution space?