a. Formulate a linear programming model for this problem
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Art Kumar lives on the outskirts of Draper and has a 1-acre lot next to his home. He plans to grow
vegetables on the lot and sell them at the downtown market during the summer. He doesn’t have
enough time to grow the vegetables himself, so he has hired a local college student to plant and
tend the garden and sell the crops at the market. Art is considering five vegetables to plant that
seem to be popular at the market—asparagus, corn, tomatoes, green beans, and red peppers. Art
estimates the following yields per acre for each vegetable—2,000 pounds of asparagus, 7,200
pounds of corn, 25,000 pounds of tomatoes, 3,900 pounds of green beans, and 12,500 pounds of
red peppers. The costs per acre are $1,800 for asparagus, $1,740 for corn, $6,000 for tomatoes,
$3,000 for green beans, and $2,700 for red peppers. Asparagus sells for $1.90 per pound, corn sells
for $0.10 per pound, tomatoes sell for $3.25 per pound, green beans sell for $3.40 per pound, and
red peppers sell for $3.45 per pound. He has budgeted $5,000 for the garden. Talking to some of
the other market vendors, he estimates that he will not sell more than 1,200 pounds of asparagus,
10,000 pounds of tomatoes, 2,000 pounds of green beans, and 5,000 pounds of red peppers. Art
wants to know the portion of his lot that he should plant with each vegetable to maximize his
revenue.
a. Formulate a linear programming model for this problem
b. Solve the model by using the computer
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
