Linear Programming Exercises: Products A and B

Exercise 2-1: Product A and B

• A company produces and sells two products, A and B, using a shared production process.
• Total available man-hours: 45,000
• Production time: Product A - 4 hours/unit; Product B - 3 hours/unit
• Market demand limits: Product A - maximum 7,000 units; Product B - maximum 10,000 units
• Profit per unit: Product A - ₹400; Product B - ₹600
• The objective is to formulate a linear programming model to maximize profit.

Exercise 2-1: XYZ Company

• XYZ Company manufactures products A and B.
• Processing time: Product A - 20 minutes/unit; Product B - 2 hours/unit
• Weekly production capacity: 80 hours
• Material requirements: Product A - 3 kg/unit; Product B - 2 kg/unit
• Market constraint for Product B: Maximum 1,500 units per week.
• The objective is to create a linear programming model for optimal production.

Exercise 2-1: Manufacturing Two Products

• Two products, A and B, are manufactured across four and six departments, respectively.
• Product A: Selling price ₹250/unit, labor cost ₹160/unit, raw material cost ₹40/unit, weekly capacity 120 units.
• Product B: Selling price ₹260/unit, labor cost ₹40/unit, raw material cost ₹40/unit. Weekly capacity is not specified.
• The goal is to formulate a linear programming problem likely focused on maximizing profit or minimizing cost given the capacity limits.

Exercise 2-1: XYZ Confectionery

• XYZ Confectionery produces Marie and Gluco biscuits.
• Marie biscuits yield a 20% profit and sell for ₹200 per box.
• Average processing time: Blending - 3 minutes; Cooking - 2 minutes; Packing - 3 minutes.
• Maximum available hours: Blending - 10 hours; Cooking - 20 hours; Packing - 15 hours.
• The objective is to formulate a linear program for maximizing biscuit box production.

Exercise 2-1: Cutting Tools Production

• Three types of cutting tools (A, B, C) are produced.
• Processing times (hours) and costs/selling prices (₹) vary across lathe, grinder, and polisher machines. See table in original problem statement for details.
• Maximum machine hours: Lathe - 50 hours; Grinder - 40 hours; Polisher - 80 hours.
• The objective is to formulate a linear programming model to maximize profit.

Exercise 2-1: Doll Manufacturing

• Three types of dolls are manufactured: Stilly, Walky, and Walky-Talky.
• Production plan: 50 Stilly, 25 Walky, 30 Walky-Talky dolls.
• Profit contributions and assembly times (hours) vary by doll type. See table in original problem statement for details.
• The objective is to formulate a linear programming model to optimize assembly time while meeting the given production plan.