Management Science and linear Programming
Assignment Instructions
Q1. A company produces two products, A and B, which have profits of $9 and $7,
respectively. Each unit of product must be processed on two assembly lines, where the
required production times are as follows:
a. Formulate a linear programming model to determine the optimal product mix that will
maximize profit.
b. Solve graphically and identify the amount of unused resources (slack) at each of the
graphical extreme points.
c. What would be the effect on the optimal solution if resource Line 1 was reduced to 40
units?
d. What would be the effect on the optimal solution if the profit for product B was increased
from $7 to $15? To $20?
2. The Bradley family owns 410 acres of farmland in North Carolina on which they grow
corn and tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest. Each
acre of tobacco costs $210 by the same token. The Bradleys have a budget of $52,500
for next year. The government limits the number of acres of tobacco that can be planted
to 100. The profit from each acre of corn is $300; the profit from each acre of tobacco is
$520. The Bradleys want to know how many acres of each crop to plant in order to
maximize their profit. Management Science and linear Programming
a) Formulate a LP model and solve.
Solve the linear programming model formulated in Problem for the Bradley family farm
graphically.
a. How many acres of farmland will not be cultivated at the optimal solution? Do the
Bradleys use the entire 100-acre tobacco allotment?
b. What would the profit for corn have to be for the Bradleys to plant only corn?
c. If the Bradleys can obtain an additional 100 acres of land, will the number of acres of
corn and tobacco they plan to grow change?
d. If the Bradleys decide not to cultivate a 50-acre section as part of a crop recovery
program, how will it affect their crop plans? APA FORMAT