## Linear Programming and Integer Linear Programming

This is my homework and it has 4 parts (A,A1), (B), (C1,C2,C3) and (D)
I have done Part A, A1 and B and its correct. they sent back part C and D and i would love it if some one can help me on part C and D

Given:

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, 3 units of Color, 15 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.

In order to meet government health regulations the manufacturer must use at least 200 units of Nutrient when it cooks a batch of X and Y. The other ingredients are in short supply, use: no more than 500 units of Color, 250 units of Flavor, 600 units of Grain

And this is my work for part A and B

PART A
1X + 2Y ≥ 200 Nutrient is Minimum because they must use at least 200.
3X + 1Y ≤ 500 Color is Maximum because 500 is the maximum available.
15X + 1Y ≤ 250 Flavor is Maximum because 250 is the maximum available.
10X + 1Y ≤ 600 Grain is Maximum because 600 is the maximum available.
PART A2
Objective function
Brand X = $100/case Brand Y = 12.5/case P = 100X + 12.5Y PART B Objective function = 100X + 12.5Y Let us pick a point from the profit line (0, 400) P = 100X + 12.5Y P = 100(0) + 12.5(400) P = 0 + 5000 P = 5000 P =$5,000