Question

Par, Inc., produces a standard golf bag and a deluxe golf bag on a weekly basis. Each golf bag requires time for cutting and dyeing and time for sewing and finishing, as shown in the following table:

Hours required per bag

Product Cutting and dyeing Sewing and finishing
standard bag 1/2 1
delux bag 1 2/3

The profits per bag and weekly hours available for cutting and dyeing and for sewing and finishing are as follows:

Product profit per unit ($)
Standard bag 10
Delux bag 8

Activity Weekly hours available
Cutting and dyeing 300
Sewing and finishing 360

Par, Inc., will sell whatever quantities it produces of these two products.

Find the mix of standard and deluxe golf bags to produce per week that maximizes weekly profit from these activities.

Answer 1

To maximize weekly profit, Par, Inc. must determine the optimal production mix of standard and deluxe golf bags, taking into account the constraints for cutting and dyeing, sewing and finishing, and profits per unit.

Step-by-step explanation:

To maximize weekly profit for Par, Inc., by determining the optimal mix of standard and deluxe golf bags, we will use linear programming. We have two products: standard bags (with a profit per unit of $10) and deluxe bags (with a profit per unit of $8). The production constraints are based on the available weekly hours for cutting and dyeing (300 hours) and for sewing and finishing (360 hours).

For standard bags, each requires 0.5 hours for cutting and dyeing and 1 hour for sewing and finishing. For deluxe bags, each requires 1 hour for cutting and dyeing and 1.5 hours for sewing and finishing. Let's denote the number of standard bags produced as x and the number of deluxe bags as y. The production constraints can be written as:

• 0.5x + y ≤ 300 (cutting and dyeing constraint)
• x + 1.5y ≤ 360 (sewing and finishing constraint)

The objective function to maximize is given by the profit equation:

• Profit = 10x + 8y

By solving this linear programming problem, possibly using the Simplex method or graphically, Par, Inc. can determine the optimal number of standard and deluxe bags to produce for maximum profit.