The Janie Gioffre Drapery Company makes three types of draperies at two differen
ID: 3141279 • Letter: T
Question
The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of standard drapes per day. At location II, it can make 20 pairs of deluxe, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 3000 pairs of deluxe drapes, 6300 pairs of better drapes, and 1800 pairs of standard drapes. If the daily costs are $750 per day at location I and $950 per day at location II, how many days should Janie schedule at each location in order to fill the orders at minimum cost? Location 1: How many days? Location 2: How many days? Minimum cost?
Explanation / Answer
Location I per day : 10 pairs of delux drapes ,20 pairs of better drapes & 13 pairs of standard drapes
Location I cost per day : $750
Location II per day : 20 pairs of delux drapes, 50 pairs of better drapes & 6 pairs of standard drapes
Location II cost per day:$950
Company wants : 3000 pairs of delux drapes ,6300 pairs of better drapes & 1800 pairs of standard drapes.
Have to find: number of days at each location inorder to fill the orders at minimum cost.
Building Equations:
Let x = cost of production , y = days of production at location I and z = days of production at location II
x = 750 y + 950 z
Let w = number of drapes needed
p= number of production of pairs of deluxe drapes
q = number of production of pairs of better drapes
r = number of production of pairs of standard drapes
W = (10p+20q+13r)y + (20p+50q+6r)z
From the question,
W = 3000p + 6300q +1800r
Comparing the coefficient of p,q and r
3000= 10 y + 20 z
6300= 20y + 50 z
1800= 13 y +6 z
Solving we get
y = 90 and z = 105
Hence number of days at location I = 90 days
number of days at location II = 105 ddays
And cost (x)= $ 144,000
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