The Oscar Drapery Company makes three types of draperies at two different locations. At location 1, it can make 10 pairs of deluxe draperies, 20 pairs of better draperies, and 13 pairs of standard drapes per day. At location 2, it can make 20 pairs of deluxe drapes, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 2000 pairs of deluxe drapes, 4200 pairs of better drapes, and 1200 pairs of standard drapes. If the daily costs are $500 per day at location 1 and $800 per day at location 2, how many days should Oscar schedule at each location in order to fill the orders at minimum cost? Find the minimum cost.

Question

The Oscar Drapery Company makes three types of draperies at two different locations. At location 1, it can make 10 pairs of deluxe draperies, 20 pairs of better draperies, and 13 pairs of standard drapes per day. At location 2, it can make 20 pairs of deluxe drapes, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 2000 pairs of deluxe drapes, 4200 pairs of better drapes, and 1200 pairs of standard drapes. If the daily costs are $500 per day at location 1 and $800 per day at location 2, how many days should Oscar schedule at each location in order to fill the orders at minimum cost? Find the minimum cost.

Answer 1

x = days at Loc 1

y = days at Loc 2
then limits and intecepts
deluxe 10x+20y >/= 2000 (0,100)(200,0)
better 20x+50y >/= 4200 (0,84)(210,0)
standard 13x+6y >/= 1200 (0,200)(92.3,0)
graph those
and cost constraint c = 500 x + 800 y
Now test upper corners
try (0,200) all loc 2
c = 800(200) = 160,000
try (210,0) all loc 1
c = 500(210) = 105,000 better
Try also the intersection of the other lines to see if you get a lower cost solution

Answer 2

To find the minimum cost and schedule at each location, we need to determine the number of days required at each location to fulfill the order while minimizing the cost.

Let's start by figuring out the number of days needed at each location to meet the order requirements.

At location 1:
- Deluxe drapes: 2000 pairs / 10 pairs per day = 200 days
- Better drapes: 4200 pairs / 20 pairs per day = 210 days
- Standard drapes: 1200 pairs / 13 pairs per day ≈ 92.31 days (round up to 93 days)

At location 2:
- Deluxe drapes: 2000 pairs / 20 pairs per day = 100 days
- Better drapes: 4200 pairs / 50 pairs per day = 84 days
- Standard drapes: 1200 pairs / 6 pairs per day = 200 days

Now, let's calculate the cost for each location.

At location 1:
Cost at location 1 = 200 days * $500 per day = $100,000

At location 2:
Cost at location 2 = 100 days * $800 per day = $80,000

Therefore, if Oscar schedules 200 days at location 1 and 100 days at location 2, the total cost would be $100,000 + $80,000 = $180,000, which is the minimum cost to fill the orders.