# Linear Programming : Objective Functions, Constraints, Feasible Area, Slack and Surplus Variables 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.

https://brainmass.com/math/linear-programming/37454

#### Solution Summary

Two linear programming problems are analyzed with respect to Objective Functions, Constraints, Feasible Area, Slack and Surplus Variables and Optimal Solutions.