IELM 202
Midterm Solution
1/6/11
1.
(a)
The optimal solution is to produce no chocolate ice cream, 300 gallons of vanilla ice
cream, and 75 gallons of banana ice cream. Total profit will be $341.25.
(b)
The optimal solution will change since $1.00 is outside the allowable range of $(0.95
0.05) to $(0.95 + 0.021429). The profit will go up, but how much can’t be determined
without resolving.
(c)
The optimal solution will not change since $0.92 is within the allowable range. The
total profit will decrease by (75)$0.03 = $2.25 to $339.
(d)
The optimal solution will change. Since the change is within the allowable range (the
allowable decrease is 3.75), we can calculate the change in profit using the shadow price
(1*3 = 3). The new profit will be $338.25.
2.
Solution for formulation:
The decision variables can be denoted and defined as follows:
M = number of men’s gloves to produce per week,
W = number of women’s gloves to produce per week,
C = number of children’s gloves to produce per week,
F = number of fulltime workers to employ,
PT = number of parttime workers to employ.
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