Linear Programming

For each of the following questions carefully answering according to the
instructions provided. Please put all of your answers on a separate
piece of paper, clearly numbering each problem. Write complete answers
(use independent ideas) to the following questions. If answering a
problem, please show your work.

1. The Dub-Dub and Dub Company produces and markets three lines of WEB
page designs: A, B, and C; A is a standard WEB page design and B and C
are professional WEB page designs. The manufacturing process for the
WEB page designs is such that two development operations are required -
all WEB page designs pass through both operations. Each WEB page design
requires 3 hours of development time in Operation 1. In Operation 2 WEB
page design A requires 2 hours of development time; WEB page design B
requires 4 hours; and WEB page design C requires 5 hours. Operation 1
has 50 hours of development time per week and Operation 2 has sufficient
manpower to support 80 hours of development per week. The market group
for Dub-Dub and Dub has projected that the demand for the standard WEB
page design will be no more than 25 per week. Because WEB page designs
B and C are similar in quality, the combined demand for those WEB page
designs has been forecast - the total demand is ten or more, but not
more than 30 per week. The sale of WEB page design A results in $7
profit while WEB page design B and C provide $8 and $8.5 profits
respectively. How many of WEB page designs A, B, and C should be
produced weekly if the company seeks to maximize profits? Formulate the
problem as a standard LP model.

2. Use the graphical method to solve the problem:

Maximize: Z = 1x1 + 1x2

Subject to: 1x1 + 2x2 ( 6

6x1 + 4x2 ( 24

3x1 +3x2 ( 21

x1 , x2 ( 0

Graph the problem.

What is the optimal solution?

What would the solution be if the third constraint were removed from the
problem?