Reference no: EM13961938
1. The Adams family owns a total of 400 acres of farmland in North Carolina on which they grow corn and tobacco. Each acre of corn costs $125 to plant, cultivate, and harvest; each acre of tobacco costs $235. The Adams family has a budget of $80,000 for next year. The government rules limit the number of acres of tobacco that can be planted to 150. The profit from each acre of corn is $240; the profit from each acre of tobacco is $450. The Adams family wants to know how many acres of each crop to plant in order to maximize their profit.
Formulate a linear programming model for this problem by determining
(a) The decision variables.
x1 = tobacco
x2 = corn
(b) The objective function.
Maximize Z = $450x1 + $240x2
(c) All the constraints.
$235x1 + $125x2 <= 80,000
x1<=150
x1+x2<=400
x1,x2>=0
Answer the following (please explain and show work):
(a) If the profit from an acre of corn increases from $240 to $300, will the number of acres of corn and tobacco planted change? Will the total profit change?
(b) The Adams family has an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for $150 per acre. Should the Adams lease the land at that price? What is the maximum price the Adams should pay their neighbor for the land, and how much land should they lease at that price?
(c) The Adams are considering taking out a loan to increase their budget. For each dollar they borrow, how much additional profit would they make? If they borrowed an additional $5,000, would the number of acres of corn and tobacco they plant change?
|
Why is lack of trust an obstacle to supply chain management
: Why is lack of trust an obstacle to Supply Chain Management? How can we overcome this obstacle? Please write in your own words
|
|
Main planning tasks performed as part of project integration
: Name the main planning tasks performed as part of project integration management? What are the main documents created, and what should they contain?
|
|
Magnetic ?eld is a vector quantity
: Magnetic ?eld is a vector quantity {vector B}, therefore, it has two components to represent it: Magnitude {B}, and direction.
|
|
Assignment to five commercial banks
: Five analyst have recently been hired for assignment to five commercial banks on one-to-one basis. The cost of each analyst in each bank is given in the following table. Determine the lowest cost of assignment.
|
|
Crop to plant in order to maximize
: The profit from each acre of corn is $240; the profit from each acre of tobacco is $450. The Adams family wants to know how many acres of each crop to plant in order to maximize their profit.
|
|
Find the optimal solution to the relaxation lp
: a) Find the optimal solution to the Relaxation LP. b) Find the optimal solution to the All-integer LP. Is it the same as that obtained in part (a)?
|
|
What is the decision facing nestle
: Marketing in action case- Real Choices at Nestle. What is the decision facing Nestle? What factors are important in understanding this decision situation? What are the alternatives
|
|
Evaluate the given iterated or double integrals
: Evaluate the following iterated or double integrals, by means of any technique you've learned so far. ∫∫R(x-y)(x2+y2+1)-1dA dx. Where R is the region bounded by the unit circle centered at the origin.
|
|
System optimal scenario
: Show that the average travel time per person is minimized if 2,000 people travel by road. This is known as the "system optimal" scenario. What percent worse than system optimal is the user-optimal scenario?
|