Skill Qualification Task 11 Linear Programming This questio

Skill Qualification Task 11 - Linear Programming This questions involves optimization.Generally our objective, in business and manufacturing problems, is to maximize profit under circumstances of resource constraints.Linear programming can also seek to minimize outcomes, say in the case of waste in a process, but here we will look to a few examples of profit maximization under resource constraints. Our examples are simple, often involving just two products and two constraints but the objective in this skill qualification task is to understand what linear programming is about. Solving these problems by hand with multiple product and constraints can become very complicated and time-consuming.

Required: First we want to write the Object Equation. Second we write the constraints (Time Constraint and Material Constraint). Three we draw the graph: Step 1 plot the Time Constraint: Step 2 pot the Material Constraint:. Step 3 - simultaneous equations. Step 4 - Test the candidate points

Question

You have opened the Hippie Outfitters Clothing Manufacturing Company and make specialized embroidered bell bottoms and skirts. The bell bottoms require 4 yards of material and 3 hours of time to make. The skirts require 3 yards of material and 5 hours of time to make (lots of embroidery). You have 420 yds of material and 450 hours available on the schedule. If the profit margin on the bell bottoms is $65 and the profit margin on the skirts is $85, how many bell bottoms and skirts should you order?   

Solution

Let B be the number of bell bottoms and S be the number of skirts

Objective

maximize

65B+85B

subject to (constraints)

Time Constraint

3B+5S=450

Material Constraint

4B+3S=420