Question

4. Given a linear programming optimization problem, with the choice of two products, we know in advance that a possible answer is to make only one product.

5. Cost minimization problems typically involve constraints which have the phrase “at least”.  

Please explain each answer in your own words

1. Please show what slack resources are graphically. You can draw a picture and scan it or take a picture and add it to the document.

2. Please given an example of a constraint for a cost minimization problem.

3. Give an example of an objective function not listed in the book.

4. Why is it important to have non-negative answers to linear programming problems?

5. What is meant by divisibility in linear programming? Explain in your own words and include an example.  

Note: You can use Excel and just paste the images of the output on to the Word document.

1. You are a hipster who has a workshop, which makes artisan cabinets out of Bocote wood. Specifically, you make chifforobes and pie safes. Each chifforobe you make earns $200 profit and each pie safe earns $150. Each chifforobes requires 150 board feet of bocote wood and 10 hours of labor. Each pie safe requires 100 board-feet of bocote wood and 15 hours of labor. Each month you have 3000 board-feet of bocote wood and 300 hours of labor.

a. How many chifforobes and pie safes should you make each month if you want to maximize your profits?

b. What if one month you run short on bocote wood and only have 1500 board-feet, how many chifforobes and pie safes should you make to maximize profits?

2. You have now tired of making artisan cabinets. You decide to use all the profits you made making cabinets to buy a farm and grow dragon carrots. Your dragon carrot farm requires an organic fertilizer mix that has at least 900 decigrams of nitrogen, 480 decigrams of phosphorus, and 15 decigrams of potassium. You have two choices of organic fertilizer: Blue Zippy and Harmonic Flash. Blue Zippy costs $20 a pound and each pound contains 50 decigrams of nitrogen, 50 decigrams of phosphorus, and 5 decigrams of potassium. Harmonic Flash $30 a pound and each pound contains 100 decigrams of nitrogen, 30 decigrams of phosphorus, and no potassium.

a. How much Blue Zippy and Harmonic Flash should you buy to meet your requirements, while minimizing cost?

b. If Harmonic Flash changed their mix to include 40 decigrams of phosphorus and 1 decigram of potassium, would you change your order? If so, how?

Answer 1