A special food for athletes is to be developed from three foods: food x, Food Y and Food Z. The new food is to contain at least 66 mg of vitamin A, at least 48 mg of Vitamin B, at least 40 mg of Vitamin C and at least 58 mg of Vitamin D. Each pound of Food X costs TK 1.50, and contains 2 mg of Vitamin A, 4 mg of Vitamin B, 1 mg of Vitamin C and 6 mg of Vitamin D. On the other hand, each pound of Food Y costs TK 2.50 and contains 9 mg of Vitamin A, 3 mg of Vitamin B, 4 mg of Vitamin C and 2 mg of Vitamin D. Whereas each pound of Food Z costs TK 2.00 and contains 7 mg of Vitamin A, 2 mg of Vitamin B, 8 mg of Vitamin C and 1 mg of Vitamin D. How many pounds of each food should be used in the mixture in order to meet these requirements at a minimum cost ? What is the minimum cost ?
A special food for athletes is to be developed from three foods: food x, Food Y and Food Z. The new food is to
contain at least 66 mg of vitamin A, at least 48 mg of Vitamin B, at least 40 mg of Vitamin C and at least 58 mg
of Vitamin D. Each pound of Food X costs TK 1.50, and contains 2 mg of Vitamin A, 4 mg of Vitamin B, 1 mg
of Vitamin C and 6 mg of Vitamin D. On the other hand, each pound of Food Y costs TK 2.50 and contains 9
mg of Vitamin A, 3 mg of Vitamin B, 4 mg of Vitamin C and 2 mg of Vitamin D. Whereas each pound of Food
Z costs TK 2.00 and contains 7 mg of Vitamin A, 2 mg of Vitamin B, 8 mg of Vitamin C and 1 mg of Vitamin D.
How many pounds of each food should be used in the mixture in order to meet these requirements at a minimum
cost ? What is the minimum cost ?
Trending now
This is a popular solution!
Step by step
Solved in 10 steps
