Benjamin Moore Company makes two types of paint, oil based paint and water based paint. It makes a profit of $2 per gallon on its oil-based paint and $4 per gallon on its water-based paint. Both paints contain two ingredients, A and B. The oil-based paint contains 90 percent A and 10 percent B, whereas the water-based paint contains 30 percent A and 70 percent B. Benjamin Moore currently has 8,000 gallons of ingredient A and 9,000 gallons of ingredient B in inventory and cannot obtain more at this time. Due to high demand, the company makes water based paint twice as much as oil based paint. Benjamin Moore wishes to use linear programming to determine the appropriate mix of oil-base and water-based paint to produce to maximize its total profit.

You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.

Writeup.

Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.

Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.

Excel.

As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.

The question below

Benjamin Moore Company makes two types of paint, oil based paint and water based paint. It makes a profit of $2 per gallon on its oil-based paint and $4 per gallon on its water-based paint. Both paints contain two ingredients, A and B. The oil-based paint contains 90 percent A and 10 percent B, whereas the water-based paint contains 30 percent A and 70 percent B. Benjamin Moore currently has 8,000 gallons of ingredient A and 9,000 gallons of ingredient B in inventory and cannot obtain more at this time. Due to high demand, the company makes water based paint twice as much as oil based paint.  Benjamin Moore wishes to use linear programming to determine the appropriate mix of oil-base and water-based paint to produce to maximize its total profit

Benjamin Moore Company makes two types of paint, oil based paint and water based paint. It makes a profit of $2 per gallon on its oil-based paint and $4 per gallon on its water-based paint. Both paints contain two ingredients, A and B. The oil-based paint contains 90 percent A and 10 percent B, whereas the water-based paint contains 30 percent A and 70 percent B. Benjamin Moore currently has 8,000 gallons of ingredient A and 9,000 gallons of ingredient B in inventory and cannot obtain more at this time. Due to high demand, the company makes water based paint twice as much as oil based paint. Benjamin Moore wishes to use linear programming to determine the appropriate mix of oil-base and water-based paint to produce to maximize its total profit.

You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.

Writeup.

Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.

After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.

Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.