Question Details

MAT 540
WEEK 7
 
In minimization LP problems the feasible region is always below the resource constraints. 
 
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Graphical solutions to linear programming problems have an infinite number of possible objective function lines. 
 
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In a linear programming problem, all model parameters are assumed to be known with certainty. 
 
 
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A linear programming problem may have more than one set of solutions.
 
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If the objective function is parallel to a constraint, the constraint is infeasible.
 
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If the objective function is parallel to a constraint, the constraint is infeasible.
 
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Surplus variables are only associated with minimization problems. 
 
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) Which of the following could be a linear programming objective function?
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The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?
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The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. 
 
 
 
Which of the following points are not feasible?
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Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?
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A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function. 
 
 
 
If this is a maximization, which extreme point is the optimal solution?
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Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?
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The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. 
 
 
 
 
 
Which of the following constraints has a surplus greater than 0?
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The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. 
 
 
 
 
The equation for constraint DH is:
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Decision variables
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In a linear programming problem, a valid objective function can be represented as
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Solve the following graphically
Max z =     3x1 +4x2 
s.t.             x1 + 2x2 ≤ 16 
                  2x1 + 3x2 ≤ 18 
                  x1    ≥ 2 
                   x2    ≤ 10
                  x1, x2 ≥ 0

Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25
 
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Consider the following linear programming problem: 
Max Z =           $15x + $20y 
Subject to:       8x + 5y ≤ 40 
                        0.4x + y ≥ 4 
                        x, y ≥ 0 
At the optimal solution, what is the amount of slack associated with the first constraint? 
 
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Max Z =    $3x + $9y 
Subject to:       20x + 32y ≤ 1600 
                        4x + 2y ≤ 240 
                        y ≤ 40 
                        x, y ≥ 0 
At the optimal solution, what is the amount of slack associated with the second constraint?
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