Linear Programming:

One Product/ One Resource

Suppose a toy manufacturer has 60 containers of plastic and wants to make and sell skateboards. The “recipe” for one skateboard requires five containers of plastic. The profit on one skateboard is $1.00. Assume that there will be customers for every skateboard produced. What is the maximum profit this manufacturer will make and how many skateboards does he need to produce?

What is Linear Programming?

Questions to be answered by Linear Programming:

Purpose of Mixture Problems

Feasible Region

How can the Optimal Production Policy be found

Common Features of Mixture Problems

One Product and One Resource: Making Skateboards

How do we graph?

Features about Feasible Region (Set):

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2.

3.

4.

Contraint Inequalities and Profit Formula

Steps to solve One Product/ One Resource Problems:

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2.

3.

Resources / Your Recipe / Profit per Item / Profit Formula / Givens / # Products / Total Profit
Popsicle Sticks
Pipe Cleaners
Construction Paper

Making Lemonade

One batch of lemonade powder requires 5 lemons, and we have 40 lemons on hand. Draw the feasible region for making lemonade powder. What is the maximum profit we can make if we clear a profit of $1.50 per batch?

Two Products/ One Resource

Suppose the toy manufacturer decides to expand production to 2 products: skateboards and dolls. Assume that most resources, excluding plastic, that are needed, such as labor, fasteners, and paint are available in unlimited quantities. Assume everything that is produced will sell. The recipe for one doll calls for 2 containers of plastic and the profit on one doll is $.55. What steps can be used to find the optimal production policy (maximum profit) for this manufacturer?

To find the Optimal Production Policy:

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2. 

3. 

4. 

Questions to be answered by the Mixture Chart?????

Mixture Chart

1.  Step 1

Resource Constraint Inequalities and Profit Formula

2.  Step 2

Graphing to Form the Feasible Region

Step 3:

Finding the Optimal Production Policy

Step 4:

The Role of the Profit Formula

1.  How does the optimal production policy change if the profit changes?

1.  $1.05 per skateboard

2.  $.40 per doll

Make a Mixture Chart

Step 1

A clothing manufacturer has 60 yards of cloth available to make shirts and decorated vests. Each shirt requires 3 yards of material and provides a profit of $5. Each vest requires 2 yards of material and provides a profit of $3.

Resource Constraint Inequalities and Profit Formula

Step 2

Graphing to Form the Feasible Region

Step 3:

Finding the Optimal Production Policy

Step 4:

Steps to solving Linear Programming Problems

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2. 

3. 

4. 

Setting Minimum Quantities for Products

The toy manufacturer keeps track of sales and the demand on a daily basis is for at least 4 skateboards and at least 10 dolls.

Step 1: Mixture Chart

Step 2: Resource constraint and profit formula.

Step 3: Draw a new feasible region.

Step 4: Find the optimal production policy.

Find the optimal production policy using the profit changes.

$1.05x+$0.40y

Must show the four steps to find the optimal production policy for each problem.

A clothing manufacturer has 60 yards of cloth available to make shirts and decorated vests. Each shirt requires 3 yards of material and provides a profit of $5. Each vest requires 2 yards of material and provides a profit of $3. Suppose the clothing manufacturer needs to make at least four shirts and six vests. Find the optimal production policy for this clothing manufacturer