Assignment #4: L.P. Solution
Due: Thursday, Feb. 12, 1998, 5:00pm, in the dropbox, Rosebrugh Building, 2nd Floor
Question#1 (5 marks). Using the graphical method, find the optimal solution and the optimal objective value of the following LP problem (submit your graph):
Maximize Z = X1 + 2X2
subject to
X1 <= 7
X2 <= 6
X1 + 3X2 <= 9
-X1 + X2 <= 2
X1 + X2 >= 1
X1 >= 0, X2 >= 0
Question#2.
A manufacturing firm is planning to produce two new products.
The available capacity on the required machines that will limit the
production output is summarized in the following table:
| Machine Type | Available Time ( in machine hours per week ) |
| Milling Machine | 500 |
| Lathe | 150 |
The numbers of machine hours required for each unit of the two products are
| Machine Type | Product 1 | Product 2 |
| Milling Machine | 10 | 5 |
| Lathe | 2 | 3 |
The sales department indicates that the sales potential for Product 1 will exceed the maximum production capacity and the sales potential for Product 2 will not exceed 30 units per week. Producing each unit of the two products will cost $1 per machine hour. The prices of both Product 1 and 2 will be $18 per unit.
(a) (5 marks). Let Xi be the units of Product i produced per week, i = 1 and 2. Show that the firm is facing solving the following LP problem:
Maximize Z = 6X1 + 10X2
Subject to
10X1 + 5X2 <= 500
2X1 + 3X2 <= 150
X2 <= 30
X1 >= 0, X2 >= 0
(b) (5 marks). Solve the LP problem in (a) using the graphical method. Submit your graph, and state clearly the optimal values of X1 and X2 and the maximum objective value.