Way of Nature Co. produces granolas marketed as being high in vitamins and miner

Question

Way of Nature Co. produces granolas marketed as being high in vitamins and minerals. An ounce of oats provides 8 milligrams of vitamin A. An ounce of quinoa provides 4 milligrams of vitamin A. An ounce of oats costs $0.05 and an ounce of quinoa costs $0.07. A box of the granola needs to contain at least 56 milligrams of vitamin A and must use no more than 3.5 ounces of oats. How many ounces of each ingredient should Way of Nature Co. use to meet this requirement and minimize cost? Formulate a linear programming model for this situation. Solve this model using graphical analysis. Display your graph and the solution parameters. Create your graph using Microsoft Word or Excel and submit it to your instructor.

Explanation / Answer

Way of Nature produces granolas high in vitamins and minerals.

i) An ounce of oats provides 8 milligrams of Vitamin A and an ounce of quinoa provices 4 milligrams of Vitamin A. A box of granola needs to contain at least 56 milligrams of Vitamin A and must contain no more than 3.5 ounces of oats

. Let weight of oats be represented by x and quinoa by y.

Thus 8x + 4y >= 56

and x<=3.5 ounces

Z = 0.05x+0.07y <= 0

To minimize cost, 3.5 ounces of oats and 7 ounces of quinoa can be used by Way of Nature & Co.

x y Z 0.05 0.07 C1 8 4 56 C2 1 0 3.5 C1 x y 7 0 0 14 C2 x y 1 0 3.5 7 Solution: X 3.5 Y 7 Z 0.665

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