order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day. Rather than order rabbit food that is custom‐blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend? a. Choose the unknowns, i.e. variables. State what they are so you know exactly what you are looking for. b. Write your OPTIMIZATION EQUATION. c. Write the constraints as a system of inequalities, usually there are several. d. Graph the system and identify the feasibility region. e. Identify the corners of the feasibility region, which will be the ordered pairs that you test in your optimization equation. f. Calculate the value of the optimization equation using each of the ordered pairs (from step 5) to determine which of them has the maximum or minimum values desired.
In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.
Rather than order rabbit food that is custom‐blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce.
What is the optimal blend?
a. Choose the unknowns, i.e. variables. State
what they are so you know exactly what
you are looking for.
b. Write your OPTIMIZATION EQUATION.
c. Write the constraints as a system of
inequalities, usually there are several.
d. Graph the system and identify the
feasibility region.
e. Identify the corners of the feasibility
region, which will be the ordered pairs
that you test in your optimization
equation.
f. Calculate the value of the optimization
equation using each of the ordered pairs
(from step 5) to determine which of them
has the maximum or minimum values
desired. State specifically what the best
result is and why.
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