Problem 1
Use this graph to answer the questions.
NOTE: DOTTED LINE IS AN OBJECTIVE FUNCTION CONTOUR, NOT PART OF THE
CONSTRAINT LINES
Maximize 28X + 35Y
Subject to:
12X + 15Y < 180
≥ 150
3X - 8Y < 0
X , Y > 0
a. What is the feasible region (I, II, III, IV, or V)?
b. Which point (A, B, C, D, or E) is optimal?
c. What is the value of the optimal solution?
d. Which constraints are binding?
e. Which slack or surplus variables is zero?
Problem 2
The TMA Company manufactures 19-inch color TV picture tubes in two
separate locations: Location I and Location II. The monthly production
capacity at Location I is 6000 tubes while that in Location II is 5000.
The picture tubes are shipped in two warehouses: Warehouse A and
Warehouse B. Each month 3000 tubes must be shipped to Warehouse A and
4000 tubes to Warehouse B. The shipping costs (in dollars per picture
tube) from the TMA plant to the warehouses are tabulated below:
From To Warehouse
A B
Location I $3 $2
Location II $4 $5
Find a shipping schedule that meets the above requirements while keeping
the total shipping cost to a minimum. Proceed as follows:
Let x = tubes shipped from Location I to Warehouse A
y = tubes shipped from Location I to Warehouse B
Formulate the objective function
Formulate the constraints
Graph the constraints and indicate the feasible set.
Identify the optimal corner point.
Ж
X
Z
ё
є
Ж
olution to the problem
Mathematics Homework Solutions
#37454
Linear Programming : Objective Functions, Constraints and Optimal Solutions
PROBLEM 1
1. Use this graph to answer the questions.
Maximize 28X + 35Y
Subject to:
12X + 15Y < 180
15X + 10Y ≥ 150
3X - 8Y < 0
X , Y > 0
a. What is the feasible region (I, II, III, IV, or V)?
b. Which point (A, B, C, D, or E) is optimal?
c. What is the value of the optimal solution?
d. Which constraints are binding?
e. Which slack or surplus variables is zero?
The TMA Company manufactures 19-inch color TV picture tubes in two separate locations: Location I and Location II. The monthly production capacity at Location I is 6000 tubes while that in Location II is 5000.
The picture tubes are shipped in two warehouses: Warehouse A and Warehouse B. Each month 3000 tubes must be shipped to Warehouse A and 4000 tubes to Warehouse B. The shipping costs (in dollars per picture tube) from the TMA plant to the warehouses are tabulated below:
From To Warehouse
A B
Location I $3 $2
Location II $4 $5
Find a shipping schedule that meets the above requirements while keeping the total shipping cost to a minimum. Proceed as follows:
Let x = tubes shipped from Location I to Warehouse A
y = tubes shipped from Location I to Warehouse B
a. Formulate the objective function
b. Formulate the constraints
c. Graph the constraints and indicate the feasible set.
d. Identify the optimal corner point.
e. State the optimal solution to the problem
Please see the attached file for the fully formatted problems.
Please see attached for other Problems.
Two linear programming problems are analyzed with respect to Objective Functions, Constraints, Feasible Area, Slack and Surplus Variables and Optimal Solutions.
What is this?
By OTA - Overall OTA Rating
Changping Wang, MA - 4.9/5
Purchase Cost Now
$2.19 CAD (was ~$11.97)
Included in Download
- Plain text response
- Attached file(s):
- Homework-1.doc
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Graphing Regions: Constraints and Corners - Sketch the region bound by the constraints and identify the corners. 2x + 3y is < or = 6 5x + 2y is < or = 10 x is > or = 0 y is > or = 0
- Linear Programming : Constraints and Objective Function - TRUE/FALSE 1. When the right-hand sides of 2 constraints are both increased by 1 unit, the value of the objective function will be adjusted by the sum of the constraints' prices
- Objective functions with constraints - An objective function is to be maximized given the following constraints: x+2y=4, x-y=1, x=0, y=0. Find the vertices of the set of feasible solutions.
- Using Lagrange multipliers to find extrema of (f) subject to the 2 constraints. - Minimize f(x,y,z)=x^2+y^2+z^2 with constraints x+2z=6 and x+y=12. Assume x,y,z are nonnegative.
- Constraints - Sketch the region determined by the constraints. Then find the minimum and maximum values of the objective function, subject to the indicated constraints. Objective function z=x Constraints x>= ...
