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, 36g of carbohydrates, and 4g of protein. The rabbits should be fed five ounces of food a day. Rather than order rabbit food that is custom-blended, it is cheaper to order Food A and Food B, and blend them for an optimal mix. Food A contains 8g of fat, 3g of carbohydrates, and .5g of protein per ounce, and costs $0.20 per ounce. Food B contains 12g of fat, 12g of carbohydrates, and 1g of protein per ounce, at a cost of $0.30 per ounce.
a. write a linear programming model that can be used to find the optimal blend of foods to minimize the cost of a 5 ounce ration.
b. what is the optimal blend of the foods a and b? what is the cost of the blend?
c. suppose the price of food A increased to 25 cents per ounce. use the sensitivity report to explain whether optimal blend of foods would change.
d. suppose the lab wants to fatten the rabbits up to study obesity and increased their daily ratio of 6 ounces of food. use the sensitivity report to explain how the cost of the daily ration would change.