Dugie Hansen is an elementary school teacher who also raise guinea pigs for supp
ID: 466017 • Letter: D
Question
Dugie Hansen is an elementary school teacher who also raise guinea pigs for supplemental income. He is trying to decide what to feed his pigs. He is considering using a combination of two popular guinea pig foods from the local pet store: Kaytee Fiesta Gourmet Diet and Oxbow Essentials Cavy Diet. He would like to feed the guinea pigs at a minimum cost while also making sure that each animal receives an adequate supply of calories and vitamins. The cost, calorie content and vitamin content of each feed is given in the table below.
Kaytee Fiesta
Oxbow Essentials
Calories (per pound)
80
100
Vitamins (per pound)
14 units
7 units
Cost (per pound)
$1.40
$1.80
Each guinea pig requires at least 800 calories per day and at least 70 units of vitamins. An additional constraint is that no more than 30% of the diet (by weight) can consist of Kaytee Fiesta, since it contains an ingredient that is toxic if consumed in too large a quantity.
Write the linear programming formulation to help Dugie determine how much of each feed he should give to the guinea pigs daily.
Kaytee Fiesta
Oxbow Essentials
Calories (per pound)
80
100
Vitamins (per pound)
14 units
7 units
Cost (per pound)
$1.40
$1.80
Explanation / Answer
Minimize the Cost
Z=1.40x1 + 1.80x2
Subject to the constraints
80x1+100x2<800
14 x1+7x2<70
x1+x2<30 percentage
x1,x2>0
Per day vitamins and calories
240x1+600<800
21x1+ 49x2<70
x1,x2x<0
Cost
4.2x1 +10.8x2<15
2.8x1+12.60x2<15.4
x1,x2>0
Explanation
800*30/100=240 buy calories from x1 as per diet
800*70/100=560 buy calories from x2 as per diet
Calories = 80 for x1 and 100 for x2 for pounds
x1=80 * 3 =240: 1.40*3=$4.2
x2=100*6=600: 1.80*6=$10.8
70 units of vitamins
70*30/100=21 buy vitamins from x1 as per diet
70*70/100=49 buy vitamins from x1 as per diet
Vitamins = 14 for x1 and 7 for x2 for pounds
x1=14 * 2 =28: 1.40*2=$2.8
x2=7*7=49: 1.80*7=$12.60
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