Solve the below:
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 pro¬cess for the WEB page designs is such that two development op¬era¬tions are required - all WEB page designs pass through both operations. Each WEB page design requires 3 hours of development time in Operation 1.
In Opera¬tion 2 WEB page design A requires 2 hours of development time; WEB page design B requires 4 hours; and WEB page design C re¬quires 5 hours. Operation 1 has 50 hours of development time per week and Op¬eration 2 has sufficient man¬pow¬er to support 80 hours of development per week. The mar¬ket group for Dub-Dub and Dub has projected that the de¬mand 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 com¬bined 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 pro¬duced 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
a. Graph the problem.
b. What is the optimal solution?
c. What would the solution be if the third constraint were removed from the problem?