In order to maintain the weight and health of rabbits that will be sold for pets, rabbits must be fed a daily diet containing a minimum of 12 grams (g) of fat, 24 grams (g) of carbohydrates, and 5 grams (g) of protein and should be fed no more than eight ounces of food a day.
There are two major products on the market you are considering: Food X and Food Y.
Food X contains 3 g of fat, 6 g of carbohydrates, and 1 g of protein per ounce, and costs $0.40 per ounce.
Food Y contains 4 g of fat, 4 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.50 per ounce.
It may be that one of these products meets all constraints set out in the problem and achieves the lowest total cost, or it may be necessary to blend Food X and Food Y to achieve an optimal mix. Use this information to answer the questions below:
Let x = number of ounces of Food X Let y = number of ounces of Food Y
1. What linear inequality, in terms of x and y, would represent the total amount of food in ounces?
2. What linear inequality would represent the total fat content?
3. What linear inequality would represent the total carbohydrate content?
4. What linear inequality would represent the total protein content?
5. In a single coordinate plane, graph the inequalities from the previous slides, including any other reasonable constraints. Shade the feasible regions, label your equations, and identify the scale on the axes. Note: to write an inequality as greater than or equal to, type >=, and for less than or equal to, type <=.
6. Write an equation that models the total cost of the food blend.
7. Using your graph from question 5 and total cost equation from question 6, determine the optimum solution to the problem – the solution that meets all constraints set out in the problem and achieves thelowest total cost. What point on the graph identifies this optimum solution?
8. Show/Explain how you know your solution is the optimum one. Discuss any concerns or qualifications that might arise in selecting this optimal solution.
9. Given that your facility can hold 250 rabbits and feed is 94% of your cost, use your minimum daily cost of feed per rabbit to determine your total expenses for each day.