Problem 1:
The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditionare takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period,. 240 hours of wiring time are avaiable and up to 140hrs of drilling time may be used. Each air conditoner sold yields a profit of $25. Each fan assembled may be sold for a $ 15profit. Formulate and solve this LP production mix suitation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach.
Problem 2:
Electrocomp's management realizes that it forgot to include twice two critical constraints.
In particular, management decides that there should be a minimum number of air conditiones produced in order to fufill a contract. Also, due to an oversupply of fans in the preceding period, a limit should be placed on the total number of fans produced.
(a) If Electrocomp decides that at least 20 air conditioners should be produced but no more than 80 fans should be produced, what would be the optional solution? How much slack or surplus is there for each of the four constraints?
(b) If Electrocomp decides that at least 30 air conditioners should be produced but no more than 50 fans should be produced, what would be the optional solution? How much slack or surplus is there for each of the four constraints at the optimal soultion?
Problem 3:
The dean of the Western College of Business must plan the school's course offerings for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs the college an average of $2,500 in faculty wages, and each graduate course costs $3,000. How many undergraduate and graduate courses should be taught in the fall so that total faculty salaries are kept to a minimum?
Problem 4:
The Battery park stable feeds and houses the horses used to pull tourist-filled carriages through the streets of Charleston's historic waterfront area. The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would like to keep the overall daily cost of feed to a minimum.
The feed mixes avaiable for the horses diet are an oat product, highly enriched grain, and a mineral product. Each of these mixes contains a certain amount of five ingredients needed daily to keep the average horse healthy. The table on this page shows these minimum requirements, units of ingredient per pound of feed mix, and costs for the three mixes.
In addition, the stable owner is aware that an overfed horse is a sluggish worker. Consequently, he determines that 6 pounds of feeds per day are the most that any horse needs to function properly. Formulate this problem and solve for the optimal daily mix of the three feeds.
| |
|
FEED MIX |
| DIET |
|
OAT |
|
ENRICHED |
|
MINERAL |
|
MINIMUM DAILY |
| REQUIREMENT |
PRODUCT |
|
GRAIN |
|
PRODUCT |
|
REQUIREMENT |
| (INGREDIENTS) |
(UNIT/LB) |
|
(UNITS/LB) |
|
(UNITS/LB) |
|
(UNITS) |
|
| A |
|
2 |
|
3 |
|
1 |
|
6 |
|
| B |
|
0.5 |
|
1 |
|
0.5 |
|
2 |
|
| C |
|
3 |
|
5 |
|
6 |
|
9 |
|
| D |
|
1 |
|
1.5 |
|
2 |
|
8 |
|
| E |
|
0.5 |
|
0.5 |
|
1.5 |
|
5 |
|
| Cost/lb |
|
$0.09 |
|
$0.14 |
|
$0.17 |
|
|
|
Problem 5:
Eddie Kelly is running for reeclection as a mayor of a small town in Alabama. Jessica Martinez, Kelly's campaign manager during this election, is planning the marketing campaign, and there is some stiff competition. Martinez has selected four ways to advertise: televisionads, radio ads, billboards, and newspaper ads.
The costs of these, the audience reached by each type of ad, and the maximum number avaiable is shown in the following table:
| TYPE OF AD |
|
COSTS PER |
|
AUDIENCE |
|
MAXIMUM |
| |
|
AD |
|
REACHED /AD |
NUMBER |
| TV |
|
$800 |
|
30,000 |
|
10 |
| Radio |
|
$400 |
|
22,000 |
|
10 |
| Billboards |
|
$500 |
|
24,000 |
|
10 |
| Newspapers |
|
$100 |
|
8,000 |
|
10 |
In addition , Martinezhas decided that there should be at least six ads on TV or radio or some combination of those two. The amount spent on billboards and newspapers together must not exceed the amount spent on TV ads. While fundraising is still continuing, the monthly budget for advertising has been set at $ 15,000. How many ads of each type should be placed to maximize the total number of people reached?