Problem I
Toby's Sporting Equipment, Inc. manufactures high-end and low end model of sporting goods. The management analyzed that if the company produces low-end model, each goods will require 7/10 hour in the cutting department, ½ hour in sewing department, 1 hour in finishing department and 1/10 in the inspection department. The high-end model will require 1 hour for cutting, 5/6 hour for sewing, 2/3 hour for finishing and ¼ hour for inspection department. The available hour for cutting is 630 hours, 600 hours for sewing, 708 hours for finishing and 135 hours for inspection department. The profit contribution for low-end model is Php10.00 and for high-end model is Php9.00 for every unit goods produced.
Task
i. What is the linear programming model for the problem
ii. Develop a spreadsheet model and find the optimal solution using excel solver. How many of each model should Fitness manufacture
iii. What is the total profit contribution of Fitness can earn with the optimal production quantities
iv. How many hours of production time will be scheduled in each department?
v. What is the slack time in each department?
Problem II
Johnson and Johnson produces products that will be sold to the market, The management required production for Baby powder and Baby soap must at least 400 units Baby powder requires 3 hour of processing time produce per unit and baby soap requires 2 ours of processing time per unit. There are 700 hours of processing time available. The objective of Johnson and Johnson is to satisfy these requirements with a minimum production cost. Production costs are 2 pesos per unit of baby powder and 3 pesos per unit of baby soap. P stand for baby powder and S stand for baby soap.
Task
Formulate the linear programming model then identify the following:
i. Objective function
ii. Constraint
iii. Non-negativity constraint.