The manager of FYZ Incorporated has been presented with some information on two
ID: 3209951 • Letter: T
Question
The manager of FYZ Incorporated has been presented with some information on two juice products…one with an apple flavor (A) and another with a banana flavor (B). She is told that the apple flavored drink costs $30 per gallon to produce while the banana flavored one is more expensive at $45 per gallon. Her supervisor asks her to create a linear program to determine how best to minimize these costs subject to the following constraints: 5A + 2B >= 100 4A + 8B >= 240 B>=20 A&B>=0 In the space provided below, craft the necessary linear program. (The general format of extra credit Problem 4 may prove useful in this regard.) Once you have crafted the lp, run it (JUST ONCE) with its sensitivity report. Then answer each of the 8 questions found below (Rows 40-62). a. What is the proper name of the last constraint listed above? (3 pts.) b. What is the optimal value of the objective function? (3 pts.) c. What are the optimal values of the two decision variables? (3 pts.) d. If the cost of B could be reduced to $42 per gallon, how many units of B would be optimal? (3 pts.) e. If the cost of B could be reduced to $42 per gallon, what would the new value of the objective function be? (3 pts.) f. What is the dual value (a.k.a.-"Shadow Price") for the RHS value of the first constraint? (3 pts.) g. What is the Range of Feasibility for the RHS value of the first constraint? (3 pts.) h. By what amount and in what direction would the objective function change if the RHS of the first constraint was loosened to 110? Please explain the rationale for your answer using (only) information from the sensitivity report. (4 pts.) The manager of FYZ Incorporated has been presented with some information on two juice products…one with an apple flavor (A) and another with a banana flavor (B). She is told that the apple flavored drink costs $30 per gallon to produce while the banana flavored one is more expensive at $45 per gallon. Her supervisor asks her to create a linear program to determine how best to minimize these costs subject to the following constraints: 5A + 2B >= 100 4A + 8B >= 240 B>=20 A&B>=0 In the space provided below, craft the necessary linear program. (The general format of extra credit Problem 4 may prove useful in this regard.) Once you have crafted the lp, run it (JUST ONCE) with its sensitivity report. Then answer each of the 8 questions found below (Rows 40-62). a. What is the proper name of the last constraint listed above? (3 pts.) b. What is the optimal value of the objective function? (3 pts.) c. What are the optimal values of the two decision variables? (3 pts.) d. If the cost of B could be reduced to $42 per gallon, how many units of B would be optimal? (3 pts.) e. If the cost of B could be reduced to $42 per gallon, what would the new value of the objective function be? (3 pts.) f. What is the dual value (a.k.a.-"Shadow Price") for the RHS value of the first constraint? (3 pts.) g. What is the Range of Feasibility for the RHS value of the first constraint? (3 pts.) h. By what amount and in what direction would the objective function change if the RHS of the first constraint was loosened to 110? Please explain the rationale for your answer using (only) information from the sensitivity report. (4 pts.)Explanation / Answer
a)
Making variables non negative
b) Optimal value of objective function is 1425
c) Optimal values of 2 decision variables is
A = 10, B = 25
d)
Allowable decrease of B is till 33. So with $42 also the number of unit B produce does not change. It will remain same
So B = 25
e) Optimal value now will be
10*30+25*42 = 1350
f)
1.875
g)
From 60 to 140
h)
A will become 0 and B will be 30
Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $A$2 A 10 0 30 82.5 7.5 $B$2 B 25 0 45 15 33 Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $C$6 100 1.875 100 40 40 $C$7 240 5.15625 240 160 32 $C$8 25 0 20 5 1E+30Related Questions
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