assumptions. 1. (15pts) Happy-Soda manufactures three types of holiday drink mix
ID: 388876 • Letter: A
Question
assumptions. 1. (15pts) Happy-Soda manufactures three types of holiday drink mixes (type1, type 2, type 3). Each type of drink mix is produced by blending together three types of ingredients (ingredient 1, ingredient 2, and ingredient 3). The sales price per gallon of the drink mixes and the purchase price of the ingredients per gallon are given in the table below: Type 1 Type 2 Type 3 Ingnd. 2 Ingnd. 3 225 173 S125 The three types of mixed drinks differ in their alcohol and juice content. Type 1 drink mix must have an average of at least 10% alcohol by weight and contain at most 1% carbon dioxide by weight. Type 2 drink mix must have an average of at least 890 alcohol by weight and contain at most 2% carbon dioxide by weight. Type 3 drink mix must have an average of at least 6% alcohol by weight and contain at most 1% carbon dioxide by weight. It costs $4 to make a gallon of any mixed drink, and Happy-Soda has the capacity to manufacture 1400 gallons of drink mixes daily and at most 500 gallons of each type of ingredient can be purchased daily. The alcohol content and the carbon dioxide amounts by weight for the ingredients are given below: Ingr 1 Ingr 2 Ingr 3 The daily demand for the drink mixes are 300 for Type 1, 200 for Type 2, and 100 for Type a Formulate an LP model that maximizes daily profits for Happy-Soda. b. Let's assume that Happy-Soda has the option of advertising the drink mixes. Each dollar spent in advertising a particular type of drink increases the daily demand by 10 gallons. What would change in the model from part a? (Do not solve.) 2. (10 pts) A bicycle manufacturing Company makesExplanation / Answer
Question 1
a) LP model is following
Let Xij be the gallons of ingredient j used in type i drink mix
Max 35(X11+X12+X13)+30(X21+X22+X23)+25(X31+X32+X33)-22.5(X11+X21+X31)-17.5(X12+X22+X32)-12.5(X13+X23+X33)-4(X11+X12+X13+X21+X22+X23+X31+X32+X33)
s.t.
0.12X11+0.06X12+0.08X13 >= 0.1*(X11+X12+X13)
0.005X11+0.02X12+0.03X13 <= 0.01*(X11+X12+X13)
0.12X21+0.06X22+0.08X23 >= 0.08*(X21+X22+X23)
0.005X21+0.02X22+0.03X23 <= 0.02*(X21+X22+X23)
0.12X31+0.06X32+0.08X33 >= 0.06*(X31+X32+X33)
0.005X31+0.02X32+0.03X33 <= 0.01*(X31+X32+X33)
X11+X12+X13+X21+X22+X23+X31+X32+X33 <= 1400
X11+X21+X31 <= 500
X12+X22+X32 <= 500
X13+X23+X33 <= 500
X11+X12+x13 <= 300
X21+X22+X23 <= 200
X31+X32+X33 <= 100
Xij >= 0
b) Revised model is following:
A new decision variable would be introduced. Objective function and three constraints will also change.
Let Ai be the amount spent in advertising drink i
Max 35(X11+X12+X13)+30(X21+X22+X23)+25(X31+X32+X33)-22.5(X11+X21+X31)-17.5(X12+X22+X32)-12.5(X13+X23+X33)-4(X11+X12+X13+X21+X22+X23+X31+X32+X33) - 4(A1+A2+A3)
s.t.
0.12X11+0.06X12+0.08X13 >= 0.1*(X11+X12+X13)
0.005X11+0.02X12+0.03X13 <= 0.01*(X11+X12+X13)
0.12X21+0.06X22+0.08X23 >= 0.08*(X21+X22+X23)
0.005X21+0.02X22+0.03X23 <= 0.02*(X21+X22+X23)
0.12X31+0.06X32+0.08X33 >= 0.06*(X31+X32+X33)
0.005X31+0.02X32+0.03X33 <= 0.01*(X31+X32+X33)
X11+X12+X13+X21+X22+X23+X31+X32+X33 <= 1400
X11+X21+X31 <= 500
X12+X22+X32 <= 500
X13+X23+X33 <= 500
X11+X12+x13-10A1 <= 300
X21+X22+X23-10A2 <= 200
X31+X32+X33-10A3 <= 100
Xij, Ai >= 0
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