1. Maribel is selling regular and special juices. To make a bottle of regular juice, she needs 2 pounds of mango and 3 pounds of pineapple. On the other hand, 4 pounds of mango and 2 pounds of pineapple are needed to make a bottle of special juice. A profit of P30 is made for a bottle of regular juice and P40 for a bottle of special juice. Maribel is currently has 800 pounds of mango and 480 pounds of pineapple. She wants to make at least 180 bottles of special juice. How many bottles of each type of juice must she make to maximize her profit? How much will be her maximum profit? 2. A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits? 3. 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?
1. Maribel is selling regular and special juices. To make a bottle of regular
juice, she needs 2 pounds of mango and 3 pounds of pineapple. On the
other hand, 4 pounds of mango and 2 pounds of pineapple are needed to
make a bottle of special juice. A profit of P30 is made for a bottle of regular
juice and P40 for a bottle of special juice. Maribel is currently has 800
pounds of mango and 480 pounds of pineapple. She wants to make at least
180 bottles of special juice. How many bottles of each type of juice must
she make to maximize her profit? How much will be her maximum profit?
2. A calculator company produces a scientific calculator and a graphing
calculator. Long-term projections indicate an expected demand of at
least 100 scientific and 80 graphing calculators each day. Because of
limitations on production capacity, no more than 200 scientific
and 170 graphing calculators can be made daily. To satisfy a shipping
contract, a total of at least 200 calculators much be shipped each day. If
each scientific calculator sold results in a $2 loss, but each graphing
calculator produces a $5 profit, how many of each type should be made
daily to maximize net profits?
3. 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?
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