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A cereal company makes a cereal from two ingredients: wheat and oats. Each ingredient provides two essential nutrients: vitamin A and vitamin B. The company wants to know how many ounces of wheat and oats to include in each box of cereal so that the minimum requirements of 48 milligrams of vitamin A and 20 milligrams of vitamin B are satisfied. An ounce of wheat provides 10.5 milligrams of vitamin A and 2.4 milligrams of vitamin B. An ounce of oats provides 6 milligrams of vitamin A and 1.8 milligram of vitamin B. An ounce of wheat costs $0.05 and an ounce of oats costs $0.10. The company wants to minimize the total cost of production.
Find the solution to this problem using the Simplex method.

Sagot :

Answer:

z (min ) = 0.4167    $

x = 8,33 oz

y = 0

Step-by-step explanation:

Table:

                              Vitamin A        Vitamin B         Cost $/oz

Wheat  (x)                10.5                    2.4                   0.05          

Oats     (y)                 6                       1.8                    0.10          

Requirements           48 (mg)              20 (mg)

Requirements           1,693 (oz)           0,7054 (oz)

The problem is minimized z subject to two constraint

z  =  0.05*x  + 0.1*y   to minimize

Subject to:

Requirement  of  Vitamin A

10.5*x + 6 * y  ≥  48

Requirement  of  Vitamin B

2.4*x   + 1.8*y ≥  20

x≥0  y≥0

Using  the on-line solver AtomZmaths and after 3 iterations the solution is:

z (min ) = 0.4167    $

x = 8,33 oz

y = 0

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