Company A produces and sells a popular pet food product packaged

Company A produces and sells a popular pet food product packagedResolved Question:Company A produces and sells a popular pet food product packaged under two brand names, with formulas that contain different proportions of the same ingredients. Company A made this decision so that their national branded product would be differentiated from the private label product. Some product is sold under the company’s nationally advertised brand (Brand Y), while the re-proportioned formula is packaged under a private label (Brand X) and is sold to chain stores.Because of volume discounts and other stipulations in the sales agreements, the contribution to profit from the Brand Y product sold to distributors under the company’s national brand is only $12.50 per case compared to $100 per case for private label product Brand X. There are four ingredients involved in this problem. The recipes specifying the use of each ingredient in the two product brands are given in the template. Also note, an ingredient may either be in limited supply or may have government regulations requiring a minimum or maximum amount of an ingredient.Brand X: $100 per case for private label product (profit)1 unit of Nutrient, 2 units of Color, 6 units of Flavor and 10 units of Grain.Brand Y: Cost $12.50 per case for distributors under the company’s national brand (profit)2 units of Nutrient, 1 unit of Color, 1 unit of Flavor and 1 unit of Grain.The ingredients are in short supply, use: no more than 500 units of nutrient ,no more than 150 units of color, no more than 400 units of flavor, and no more than 300 units of grainI need to determine the optimum production number of cases for brand x and y that yields the greatest amount of profit .determine how many cases of brand x should be produced during each production period.Detrmine how many cases of band y should be produced during each production period, and explain how the feasible region on my graph was used