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

To find the minimum cost, we need to determine the number of days Oscar should schedule at each location.

Let's start by setting up the variables:

Let D1 = number of days scheduled at location 1
Let D2 = number of days scheduled at location 2

Now, we can set up the equations to represent the production capacity at each location:

For deluxe draperies:
Location 1: 10 pairs per day * D1 days = 10D1 pairs
Location 2: 20 pairs per day * D2 days = 20D2 pairs

For better draperies:
Location 1: 20 pairs per day * D1 days = 20D1 pairs
Location 2: 50 pairs per day * D2 days = 50D2 pairs

For standard drapes:
Location 1: 13 pairs per day * D1 days = 13D1 pairs
Location 2: 6 pairs per day * D2 days = 6D2 pairs

Now let's set up the equations to represent the demand for each type of drapery:

Deluxe drapes demand: 2000 pairs
Better drapes demand: 4200 pairs
Standard drapes demand: 1200 pairs

So, we have the following equations:

10D1 + 20D2 = 2000 (deluxe drapes)
20D1 + 50D2 = 4200 (better drapes)
13D1 + 6D2 = 1200 (standard drapes)

To find the minimum cost, we need to determine the values of D1 and D2 that satisfy these equations and minimize the cost.

Next, let's consider the cost of each location:

Cost at location 1: $500 per day
Cost at location 2: $800 per day

The total cost can be calculated as follows:

Total cost = Cost at location 1 x D1 + Cost at location 2 x D2

To minimize the cost, we will use linear programming techniques, such as the Simplex Method or graphical methods, to solve this system of equations and find the values of D1 and D2 that satisfy the constraints and minimize the total cost.

Once we have the values of D1 and D2, we can substitute them back into the cost equation to find the minimum cost.