1. A manufacturing company sells two products that are A and B at 25$ and 20$ respectively.
The company has only 1800 resource units available every day. Product A requires 20
resource units while Product B requires 12 resource units and both the products require a
production time of 4 minutes. The total available working hours available in a day are 8. What
should be the production quantity for each of the products to maximize profits.
2. Professor Hamer is on a low cholesterol diet. During lunch at the college cafeteria, he always
chooses between two meals, Pasta or Tofu. The table below lists the amount of protein,
carbohydrates, and vitamins each meal provides along with the amount of cholesterol he is
trying to minimize. Mr. Hamer needs at least 200 grams of protein, 960 grams of
carbohydrates, and 40 grams of vitamins for lunch each month. Over this time period, how
many days should he have the Pasta meal, and how many days the Tofu meal so that he gets
the adequate amount of protein, carbohydrates, and vitamins and at the same time
minimizes his cholesterol intake?
3. Niki holds two part-time jobs, Job I and Job II. She never wants to work more than a total of 12
hours a week. She has determined that for every hour she works at Job I, she needs 2 hours
of preparation time, and for every hour she works at Job II, she needs one hour of preparation
time, and she cannot spend more than 16 hours for preparation. If she makes $40 an hour at
Job I, and $30 an hour at Job II, how many hours should she work per week at each job to
maximize her income?
4. Professor Symons wishes to employ two students, John and Mary, to grade the homework
papers for his classes. John can mark 20 papers per hour and charges $5 per hour, and Mary
can mark 30 papers per hour and charges $8 per hour. Each student must be employed at
least one hour a week to justify their employment. If Mr. Symons has at least 110 homework
papers to be marked each week, how many hours per week should he employ each student to
minimize his cost?
5. A diet is to contain at least 2400 units of vitamins, 1800 units of minerals, and 1200 calories.
Two foods, Food A and Food B are to be purchased. Each unit of Food A provides 50 units of
vitamins, 30 units of minerals, and 10 calories. Each unit of Food B provides 20 units of
vitamins, 20 units of minerals, and 40 calories. If Food A costs $2 per unit and Food B cost $1
per unit, how many units of each food should be purchased to keep costs at a minimum?
6. An oil company has two refineries. Each day, Refinery A produces 200 barrels of high-grade
oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $12,000 to
operate. Each day, Refinery B produces 100 barrels of high-grade oil, 100 barrels of medium-
grade oil, and 200 barrels of low-grade oil and costs $10,000 to operate. The company must
produce at least 800 barrels of high-grade oil, 900 barrels of medium-grade oil, and 1,000
barrels of low-grade oil. How many days should each refinery be operated to meet the goals
at a minimum cost?
7. A farmer has 100 acres of land on which she plans to grow wheat and corn. Each acre of
wheat requires 4 hours of labor and $20 of capital, and each acre of corn requires 16 hours of
labor and $40 of capital. The farmer has at most 800 hours of labor and $2400 of capital
available. If the profit from an acre of wheat is $80 and from an acre of corn is $100, how
many acres of each crop should she plant to maximize her profit?
