Operations Research - Linear Programming ANSWERS/SOLUTIONS (WITH R)

Step by step Solutions and Answers to Operations Research - Modeling with Linear Programming and Minimization Models. The solutions are done using the R programming language along with the diagrams and graphs. To view the step by step method on how I did this view my website: http://blog.jamesgalaxy.com/operations-research-linear-programming-answers-solutions-with-r/

Set 2.2a Question 6

Alumco manufactures aluminium sheets and aluminium bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 580 bars . The profit per ton is $40 per sheet and $35 per bar. Determine the the optimal daily production mix.

Set 2.2a - Question 9

ChemLabs uses raw materials I and II to produce two domestic cleaning solutions, A and B. The daily availabilities of raw materials I and II are 150 and 145 units, respectively. One unit of solution A consumes .5 unit of raw material I and .6 unit of raw material II, and one unit of solution B uses .5 unit of raw material I and .4 unit of raw material II. The profits per unit of solutions A and B are $8 and $10, respectively. The daily demand for solution A lies between 30 and 150 units, and that for solution B between 40 and 200 units. Find the optimal production amounts of A and B.

Set 2.2a - Question 12

Wild West produces two types of cowboy hats. A type 1 hat requires twice as much labor time as a type 2. If the all available labor time is dedicated to Type 2 alone, the company can produce a total of 400 Type 2 hats a day. The respective market limits for the two types are 150 and 200 hats per day. The profit is $8 per Type 1 hat and $5 per Type 2 hat. Determine the number of hats of each type that would maximize profit.

Set 2.2a - Question 13

Show & sell can advertise its products on local radio or television(TV). The advertisement budget is limited to $10,000 a month. Each minute of radio advertisement costs $15 and each minute of TV commercials costs $300. Show & sell likes to use radio advertisement at least twice as much as TV. In the menatime, it is not practical to use more than 400 minutes of radio advertisement a month. Past experience shows that TV advertisement is estimated to be 25 times more effective than that of radio. Determine the optimum allocation of the budget to radio and TV advertising

Minimization Model 2.2B - Q4

John must work at least 20 hours a week to supplement his income while attending school. He has the opportunity to work in two retail stores. In store 1, he can work between 5 and 12 hours a week, and in store 2 he is allowed between 6 and 10 hours. Both stores pay the same hourly wage. In deciding how many hours to work in each store, John wants to base his decision on work stress. Based on interviews with present employees, John estimates that, on an ascending scale of 1 to 10, the stress factors are 8 and 6 at stores 1 and 2, respectively. Because stress mounts by the hour, he assumes that the total stress for each store at the end of the week is proportional to the number of hours he works in the store. How many hours should 10hn work in each store?