Homework SourseTwo of the ingredients oats and rice provide vitamins A and
Two of the ingredients, oats and rice, provide vitamins A and B. How many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 45 milligrams of vitamin A and 13 milligrams of vitamin B while minimizing cost. An ounce of oats contributes 10 milligrams of vitamin A and 2 milligram of vitamin B, whereas an ounce of rice contributes 6 milligrams of A and 3 milligrams of B. An ounce of oats costs $0.06, and an ounce of rice costs $0.03.
What is the optimal objective function value?
Thx
| Write all the vertices of the feasible region and identify the optimal vertex | ||||||||||||||||
| What is the optimal objective function value?
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Solution
Let us graph this to find the vertices
Vertices are
OPtimal mix is (0 oats and 7.5 mg rice)
Minimum cost = 0.225
| Oats | Rice | ||
| Vit A | 10mg | 6mg | 45 |
| Vit B | 2mg | 3mg | 13 |
| Price | 0.06 | 0.03 | |
| Objective is to minimise | 0.06x1+0.03x2 | ||
| x1 | no of mg of oats | ||
| x2 | no of mg of rice | ||
| Constraints: | |||
| 10x1+6x2>=45 | |||
| 2x1+3x2>=13 |
