Answer:
Let x ounce of chicken and y ounce of tofu were taken,
∵ One ounce of chicken provides 35 Calories and 8.5 g of protein,
So, in x ounces of chicken
Calories = 35x, Â Protein = 8.5x grams,
Now, One ounce of tofu provides 20 Calories and 2.5 g of protein.
So, in y ounces of tofu,
Calories = 20y and protein = 2.5y grams,
Thus, the total calories = 35x + 20y,
Total protein = 8.5x + 2.5y
According to the question,
35x + 20y ≥ 300 -----(1),
8.5x + 2.5y ≥ 48 ----(2),
Now, the cost of a pound for chicken = $ 5,
So, the cost of 16 ounces of chicken = $ 5  ( ∵ 1 pound = 16 ounces ),
⇒ the cost of 1 ounces of chicken = [tex]\frac{5}{16}[/tex] dollars,
Similarly, the cost of a pound of tofu = $ 2.5,
So, the cost of 1 ounces of tofu = [tex]\frac{2.5}{16}[/tex] dollars,
Thus, the total cost of x ounces of chicken and y ounces of tofu
[tex]C=\frac{5}{16}x+\frac{2.5}{16}y[/tex]
Now, by graphing the above constraints ( by equation (1) and (2) )
We get a feasible region that shows the possible values of x and y,
The boundary points of the feasible region are,
(2.545, 10.545), (0, 19.2), (8.571, 0)
[tex]C=\frac{5}{16}\times 2.545+\frac{2.5}{16}\times 10.545 = 2.443[/tex]
[tex]C=\frac{5}{16}\times 0+\frac{2.5}{16}\times 19.2 = 3[/tex]
[tex]C=\frac{5}{16}\times 8.571+\frac{2.5}{16}\times 0 = 2.678[/tex]
Hence, the minimum cost is $ 2.443,
For which 2.545 ounces of chicken and 10.545 ounces of tofu should be eaten.
