Maximizing Total Annual Return
Part a
The optimal solution for the solution is 5* 523.364486 + 8*1532.71028.
The value of the total annual return is 14878.50467.
Variable Cells 



Final 
Reduced 
Objective 
Allowable 
Allowable 

Cell 
Name 
Value 
Cost 
Coefficient 
Increase 
Decrease 

$D$3 
Shares of Petroluem Inc. 
523.364486 
0 
5 
12.33333333 
0.636363636 

$D$4 
Shares of Quality Steel 
1532.71028 
0 
8 
1.166666667 
5.692307692 
Part b
The constraints Funds available and Risk Maximum are binding.
The objective’s for Funds available
and Risk maximum are the binding. Both the objectives are being used to the maximum value’s.


Final 
Shadow 
Cell 
Name 
Value 
Price 
$F$5 
100000 
0.138317757 

$H$5 
800 
1.308411215 

$J$3 
Shares of Petroluem Inc. 
523.364486 
0 
Part c
The shadow price for “Funds available” is 0.1383. The shadow price for Risk maximum is 1.3084. Hence unit increase in the prices of the constraints would increase the “Funds available” by 0.1383 and “Risk Maximum” by 1.3084.
Part d
The shadow price for Petroleum Inc. maximum is 0. Hence, any additional increase in the amount invested in Petroleum Inc. maximum would result in no increase in total annual return. Thus, investment in Petroleum Inc would not be beneficial.


Final 
Shadow 
Cell 
Name 
Value 
Price 
$F$5 
100000 
0.138317757 

$H$5 
800 
1.308411215 

$J$3 
Shares of Petroluem Inc. 
523.364486 
0 
Answer 2
Part a
The optimal solution for the solution is 2* 315.9565217 + 2.25 * 136.173913
The value of the total return based on the optimal solution is 938.3043478.
Variable Cells 



Final 
Reduced 
Objective 
Allowable 
Allowable 

Cell 
Name 
Value 
Cost 
Coefficient 
Increase 
Decrease 

$D$3 
Jars Produced O 
315.9565217 
0 
2 
7 
0.392857143 

$D$4 
Jars Produced F 
136.173913 
0 
2.25 
0.55 
1.75 
Part b
The constraints Whole Tomatoes and Tomato Sauce are binding.
The objective’s for Whole Tomatoes is
and for Tomato Sauce is are the binding.
Both the objectives are being used to the maximum value’s.
Constraints 



Final 
Shadow 
Constraint 
Allowable 
Allowable 

Cell 
Name 
Value 
Price 
R.H. Side 
Increase 
Decrease 

$G$5 
2533 
0.304347826 
2533 
114 
783 

$J$5 
1400 
0.119565217 
1400 
626.4 
266 

$M$5 
588.3043478 
0 
623 
1E+30 
34.69565217 
Part c
The shadow price for “Whole Tomatoes” is 0.304348. The shadow price for “Tomato Sauce” is 0.119565. Hence unit increase in the value of the constraints would increase the “Whole Tomatoes” by 0.304348 and “Tomato Sauce” by 0.119565.
Part d
The right hand side ranges for Chopped Onions and jalapenos is 0 to 588.3043478. However, any increase in Chopped Onions and jalapenos would result in no increase in the optimal solution. Thus, there is no need to increase the amount of Chopped Onions and jalapenos.
Constraints 



Final 
Shadow 
Constraint 
Allowable 
Allowable 

Cell 
Name 
Value 
Price 
R.H. Side 
Increase 
Decrease 

$G$5 
2533 
0.304347826 
2533 
114 
783 

$J$5 
1400 
0.119565217 
1400 
626.4 
266 

$M$5 
588.3043478 
0 
623 
1E+30 
34.69565217 
Answer 3


Final 
Reduced 
Objective 
Allowable 
Allowable 
Cell 
Name 
Value 
Cost 
Coefficient 
Increase 
Decrease 
$D$3 
4888.888889 
0 
10 
5 
10 

$D$4 
Units Invested M 
1666.666667 
0 
4 
1E+30 
1.333333333 
Part a
From the solution it is seen that the Allowable increase for Units invested S is 5. Thus an increase in the Units Invested in S by units would not change the optimum solution for its present value of S = 4888.88 and M = 1666.666.
Part b
From the solution it is seen that the Allowable increase for Units invested M is 1E+30. Thus an increase in the Units Invested in M by units would not change the optimum solution for its present value of S = 4888.88 and M = 1666.666.
Part c
The allowable increase for “units purchased in stock fund” is 5 and for “units purchased in money market fund” is 1E+30. Thus increasing “units purchased in stock fund” from 10 to 12 and “units purchased in money market fund” from 4 to 6 would not change the optimum number of units purchased. Although, the total number of units purchased would increase.