1. The Marriott Tub Company manufactures two lines of bathtubs, called model A and model B. Every tub require company has available a total of 25,000 pounds of steel and 6,000 pounds of zinc. Each model A bathtub require pounds of zinc, and each yields a profit of $90. Each model B bathtub can be sold for a profit of $70; it in turn re zinc. Find the best production mix of the bathtubs
A
B
Usage
Steel Zinc
125 20
100 30
Profit
90
70
200
0
Decision Variable
25000 4000
<= <= 18000
and model B. Every tub requires a certain amount of steel and zinc; the c. Each model A bathtub requires a total of 125 pounds of steel and 20 for a profit of $70; it in turn requires 100 pounds of steel and 30 pounds of
Available Difference 25000 0 6000 2000 Maximize Profit
2. The Sweet Smell Fertilizer Company markets bags of manure labeled "not less than 60 pounds dry weight." T combination of compost and sewage wastes. To provide good-quality fertilizer, each bag should contain at leas but no more than 40 pounds of sewage. Each pound of compost costs Sweet Smell 5 cents and each pound of s a graphical LP method to determine the least cost blend of compost and sewage in each b
Decision Variable Price Constraint
Compost 30 5 >=30
Sewage 30 4 <=40
60 270
Total Minimize total cost
ss than 60 pounds dry weight." The packaged manure is a , each bag should contain at least 30 pounds of compost mell 5 cents and each pound of sewage costs 4 cents. Use of compost and sewage in each bag.
mize total cost
3. The advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure pos advertising budget ceiling placed upon it. To do so, the agency needs to decide how much of the budget to spen television spots during the afternoon hours and (2) large ads in the city's Sunday newspaper. Each television spo costs $1,250. The expected exposure, based on industry ratings, is 35,000 viewers for each TV commercial and advertisement. The agency director, Mavis Early, knows from experience that it is important to use both media i potential Breem customers. She decides that at least 5 but no more than 25 television spots should be ordered; contracted. How many times should each of the two media be used to obtain maximum exposure while staying to solve.
TV Decision Variable Price
5 3000
Views
35000
Conditions min max
Print 68 1250
Usage 100000
<=
20000 Objective Maximize
5 25
10 nil
o get the best exposure possible for the product within the $100,000 much of the budget to spend on each of its two most effective media: (1) wspaper. Each television spot costs $3,000; each Sunday newspaper ad or each TV commercial and 20,000 readers for each newspaper mportant to use both media in order to reach the broadest spectrum of on spots should be ordered; and that at least 10 newspaper ads should be um exposure while staying within the budget? Use the graphical method
Available 100000
1535000
Androgynous Bicycle Company (ABC) has the hottest new products on the upscale toy market -- boys' and girls' hubs and axles, shell design safety tires, a strong padded frame, chrome-plated chains, brackets and valves, and market for high-quality toys for the newest baby boomers, ABC can sell all the bicycles it manufactures at the fo -- $175. This is the price payable to ABC at its Orlando plant.
The firm's accountant has determined that direct labor costs will be 45% of the price ABC receives for the boys' girls' model. Production costs other than labor, but excluding painting and packaging, are $44 per boys' bicycle a packaging are $20 per bike, regardless of model.
The Orlando plant's overall production capacity is 390 bicycles per day. Each boy's bike requires 2.5 labor hours ABC currently employs 120 workers, who each put in an 8-hour day. The firm has no desire to hire or fire to affec workforce is one of its biggest assets. Using a graphical approach, determine the best product mix for ABC.
Boys
Girls
Selling Price
220
175
Quantity (DV)
240
150
Direct labor Production costs Painting and packaging
99 44 20
70 30 20
Profit
57
55
2.5
2.4
Labor hrs Total Profit per day (objec
21930
390 <=
960 <=
y market -- boys' and girls' bikes in bright fashion colors, with oversized s, brackets and valves, and a nonslip handlebar. Due to the seller's s it manufactures at the following prices; boys' bikes -- $220, girls' bikes
ABC receives for the boys' model and 40% of the price received for the are $44 per boys' bicycle and $30 per girls' bicycle. Painting and
ke requires 2.5 labor hours and each girl's model, 2.4 hours, to complete. esire to hire or fire to affect labor availability, for it believes its stable product mix for ABC.
390 (capacity constraint)
960
A company produces beer and ale. Beer sells for $7 per barrel, and ale sells for $3 per barrel. Producing a barrel corn and 2 pounds of hops. Producing a barrel of ale requires 2 pounds of corn and 1 pound of hops. The compan pounds of hops. Use Graphical and Solver maximize the company’s total revenue.
Selling Price Qty (DV) Corn Hops
Maximize Revenue
Beer 7 5
Ale 3 25
5 2
2 1
110
Usage 75 35
<= <=
Available 75 35
barrel. Producing a barrel of beer requires 5 pounds of ound of hops. The company has 75 pounds of corn and 35
6. The A-B-C department of a large company makes three products (A, B and C). The department is preparing fo is just before the annual two-week vacation during which the entire department shuts down. The manager want the three raw materials used to fabricate products A, B and C. A B= Quantity of Product B C= Quantity of Product C
A
DV Margin Mat 1 Mat 2 Mat 3
B
C
112
0
48
12
15
14
3 2 4
5 0 6
8 3 4
Objective maximize margin
Usage 720 368 640
<= <= <=
department is preparing for its final run next week, which down. The manager wants to use up existing stocks of A= Quantity of Product
2016
720 600 640
Maximize Z=12A +15B +14C Subject to Material 1 3A + 5B +8C < 720 pounds Material 2 2A +3C < 600 pounds Material 3 4A + 6B +4C < 640 pounds
nds nds nds
Dwight and Hattie have run the family farm for over thirty years. They are currently planning the mix of crops to for the upcoming season. The table below gives the labor hours and fertilizer required per acre, as well as the to each of the potential crops under consideration. Dwight, Hattie, and their children can work at most 6,500 total season. They have 20 tons of fertilizer available. What mix of crops should be planted to maximize the family’s t a linear programming model in a spreadsheet.
Acre of plantantion (Decision Variable)
Labor Required
Fertilizer Required
Expected Profit
(hours per acre)
(tons per acre)
(per acre)
Oats
50
1.5
$500
13.333333333
Wheat
60
2
$600
0
105
4
$950
0
666.666667 <=
20 <=
6500
20
Crop
Corn Usage Available
6666.66667 13.3333333 <= 120
anning the mix of crops to plant on their 120-acre farm per acre, as well as the total expected profit per acre for work at most 6,500 total hours during the upcoming to maximize the family’s total profit. Formulate and solve
The kitchen manager for Sing Prison is trying to decide what to feed its prisoners. She would like to offer some c oranges. The goal is to minimize cost, subject to meeting the minimum nutritional requirements imposed by law content of each food, along with the minimum nutritional requirements, are shown below. What diet should be fe and solve a linear programming model in a spreadsheet. Milk
Navy
Oranges
Beans
(large Calif.
(gallons)
(cups)
Valencia)
Niacin (mg)
3.2
4.9
0.8
15.5
>=
Thiamin (mg)
1.12
1.3
0.19
4.09
>=
Vitamin C (mg) 32
0
93
93
>=
Cost ($)
2
0.2
0.25
DV (QTY)
0
3
1
Total Cost (Minimze objective)
0.85
Total given
would like to offer some combination of milk, beans, and uirements imposed by law. The cost and nutritional low. What diet should be fed to each prisoner? Formulate
Minimum Daily Requirement 13 1.5 45
Maggie Stewart loves deserts, but due to weight and cholesterol concerns, she has decided that she must plan h two possible desserts she is considering, snack bars and ice cream. After reading the nutrition labels on the snac she learns that each “serving” of a snack bar weight 37 grams and contains 120 calories and 5 grams of fat. Eac 65 grams and contains 160 calories and 10 gram of fat. Maggie will allow herself no more than 450 calories and desserts, but because she loves desserts so much, she requires at least 120 grams of dessert per day. Also, she gram of each dessert, where 0 is the lowest and 100 is the highest. She assigns a taste index of 95 to ice cream she prefers ice cream to snack bars). What should her daily dessert plan be to stay within her constraints and m dessert?
Snack Bar Srving size Energy Fat
Qty (DV)
Ice Cream
37 120 5
65 160 10
85
95
1
2
167 >= 440 <= 25 <=
Tates index (maximize)
15495
cided that she must plan her dessert carefully. There are nutrition labels on the snack bar and ice cream packages, ies and 5 grams of fat. Each serving of ice cream weight more than 450 calories and 25 grams of fat in her daily dessert per day. Also, she assigns a “taste index” to each e index of 95 to ice cream and 85 to snack bars (because thin her constraints and maximize the local taste of her
max 120 450 25
The marketing group for a cell phone manufacturer plans to conduct a telephone survey to determine consum phone that is currently under development. In order to have a sufficient sample size to conduct the analysis, young males (under age 40), 150 older males (over age 40), 120 young females (under age 40), and 200 old $1 to make a daytime phone call and $1.50 to make an evening phone call (due to higher labor costs). This c anyone answers the phone. The table below shows the likelihood of a given customer type answering each p conducted with whoever first answers the phone. Also, because of limited evening staffing, at most one-third evening phone calls. How should the marketing group conduct the telephone survey so as to meet the samp possible cost?
Who Answers?
Daytime Calls Evening Calls
Day time placed
nigh time placed
Total
55.6 83.4
44.4 66.6
100 150
20%
111.2
44.4
155.6
35%
25%
No Answer
20%
5%
194.6 111.2
55.5 11.1
250.1 122.3
Number of calls
556
222
Cost of call
1.00
1.50
Young Male
10%
20%
Older Male
15%
30%
Young Female
20%
Older Female
Total Cost
889
778 259.333333
ey to determine consumer attitudes toward a new cell o conduct the analysis, they need to contact at least 100 er age 40), and 200 older females (over age 40). It costs gher labor costs). This cost is incurred whether or not type answering each phone call. Assume the survey is ffing, at most one-third of phone calls placed can be o as to meet the sample size requirements at the lowest
>= >=
100 150
>=
120
>=
200
