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MAT 540
WEEK 7
 
A linear programming problem may have more than one set of solutions.
 
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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 model consists of only decision variables and constraints.
 
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If the objective function is parallel to a constraint, the constraint is infeasible.
 
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A feasible solution violates at least one of the constraints. 
 
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Surplus variables are only associated with minimization problems. 
 
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If the objective function is parallel to a constraint, the constraint is infeasible.
 
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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 objective function?
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Decision variables
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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 minutefs 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*. 
 
 
 
This linear programming problem is a:
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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 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 her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) 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 objective function?
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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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The linear programming problem:
 
MIN Z =          2x1 + 3x2 
Subject to:       x1 + 2x2 ≤ 20 
                        5x1 + x2 ≤ 40 
                        4x1 +6x2 ≤ 60 
                        x1 , x2 ≥ 0 ,
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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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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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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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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. 
 
 
 
What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your answer in decimal notation.
 
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