Question

Peg and Al Fundy have a limited food budget, so Peg is trying to feed the family as cheaply as possible. However, she still wants to make sure her family members meet their daily nutritional requirements. Peg can buy two foods. Food 1 sells for $7 per pound and, each pound contains 3 units of vitamin A and 1 units of vitamin C. Food 2 sells for $1 per pound, and each pound contains 1 unit of each vitamin. Each day, the family needs at least 12 units of vitamin A and 6units of vitamin C.
(a) Verify that Peg should purchase 12 units of food 2 each day and thus oversatisfy the vitamin C requirement by 6 units.


(b )Al has put his foot down and demanded that Peg fulfill the family’s daily nutritional requirement exactly by obtaining precisely 12 units of vitamin A and 6 units of vitamin C. The optimal solution to new problem will involve ingesting less vitamin C, but it will be more expensive. Why?

Answer 1

Answer:

A) we requiere to fulfill the Vitamint contrains or surpass them A => 12 C=>6

B) we request that instead of fullfilling the vitaming requirement to be 12/6 or more

to be exactly for this amount.

Explanation:

We set up the situation in excel Solver with the following constraing:

     1        2      3      4

A    3 3 1 7

B    3 1 1 1

C        12 6 24

C2 = A1*A2 + B1*B2

C3 = A1*A3 + B1*B3

C4 = A1*A4 + B1*B4

common constraing:

C4 min

A1 = integer

B1 = integer

A) constraing

C2 => 12

C3 =>6

B) contraing to achieve the exact value for each vitamin:

C2 = 12

C3 =  6