2-14:

Solve the following LP problem by using Excel:

Maximize profit = 4X + 5Y

Subject to the constraints:

5X + 2Y 40

3X + 6Y 30

X 7

2X - Y 3

X, Y 0

2-18:

Solve the following LP problem by using Excel:

Minimize cost = 4X + 7Y

Subject to the constraints:

3X + 6Y 100

10X + 2Y 160

2Y 40

2X 75

X, Y 0

2-26:

A furniture cabinet maker produces two types of cabinets that house and hide televisions. The Mission-style cabinet requires $340 in materials and 15 labor hours to produce, and it yields a profit of $910 per cabinet. The Rustic-style cabinet requires $430 in materials and 20 hours to produce, and it yields a profit of $1,200. The firm has a budget of $30,000 to spend on materials. To ensure full employment, the firm wishes to maximize its profit but at the same time to keep all 30 workers fully employed, so all 1,200 available labor hours must be used. What is the best combination of furniture cabinets?

2-29:

A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% frothed milk, and 0.5 cups of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of frothed skim milk, and no whipped cream. The airline makes a profit of $1.58 on each regular latte and 1.65 on each low-fat latte, and each plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. Assuming all lattes that are made can be sold, what would be the ideal mix of regular and low-fat lattes to maximize profit for the airline?

2-40:

A photocopy machine company produces three types of laser printers - the Print Jet, the Print Desk, and the Print Pro. They earn profits of $60, $90, and $73 respectively. The Print Jet requires 2.9 hours of assembly time and 1.4 hours of testing time. The Print Desk requires 3.7 hours of assembly time and 2.1 hours of testing time. The Print Pro requires 3 hours of assembly time and 1.7 hours of testing time. The company wants to ensure that Print Desk constitutes at least 15% of the total production and Print Jet and Print Desk together constitute at least 40% of the total production. There are 3,600 hours of assembly time and 2,000 hours of testing time available for the month. What combination of printers should be produced to maximize profits?

3-5: A furniture maker sells three styles of cabinet: Italian, French, and Caribbean. All require carpentry, painting, and finishing. The owner must deliver at least 60 cabinets of each style to his distributor. Determine the product mix should he produce to maximize his profit given the following information:

Cabinet Style	Carpentry	Painting	Finishing	Profit
Italian	3.00	1.50	0.75	$72
French	2.25	1.00	0.75	$65
Caribbean	2.50	1.25	0.85	$78
Available Hours:	1,360	700	430

3-11: A grocery chain wants to promote the sale of a new flavor of ice cream by issuing up to 15,000 coupons by mail to preferred customers. The budget for this promotion has been limited to $12,000. The table below shows the expected increased sales per coupon and the probability of coupon usage for the various coupon amounts being considered.

Coupon Amount	Increased Sales Per Coupon (Cartons of Ice Cream)	Probability Coupon Will Be Used
$1.00	1.50	0.80
$0.85	1.40	0.75
$0.70	1.25	0.60
$0.55	1.00	0.50
$0.40	0.90	0.42

For example, every $1-off coupon issued will stimulate sales of 1.5 additional cartons of ice cream. However, since the probability that a $1-off coupon will actually be used is only 0.80, the expected increased sales per coupon issued is 1.2 (=0.8 x 1.5 cartons).

The selling price per carton of ice cream is $3.50 before the coupon value is applied. The chain wants at least 20% of the coupons (3000 coupons) issued to be of the $1-off variety and at least 10% of the coupons issued to be of each of the other four varieties (1500 coupons each). What is the optimal combination of coupons to be issued, and what is the expected net increased revenue from this promotion?

3-20: An airline in southern California needs ticket counter staff to work six-hour long shifts. Some speak English as a first language, and some are fully bilingual in English and Spanish. The airline believes demand for ticket agents will be as follows:

	6-9am	9am-noon	noon-3pm	3pm-6pm	6pm-9pm
Agents Needed	12	20	16	24	12

All agents take six-hours shifts, so no one starts at 6pm. At least half of the agents at any time are expected to speak English as a first language, and at least one quarter must be fully bilingual at all times.

a) How many and what type of agents should be hired for each shift to meet the language and staffing requirements, so that the total number of agents is minimized?

b) What is the optimal hiring plan if English-only agents are paid $25 an hour, and bilingual agents are paid $29 an hour? Does the plan change from what is computed in part a?

3-24: The owner of a private freighter is trying to decide which cargo he should carry on his next trip. He has two choices of cargo, which he can agree to carry in any combination.

He has available to carry up to 15 tons of cargo A, which takes up 675 cubic feet per ton and earns revenue of $85 per ton. Or, he may also carry up to 54 tons of cargo B, with a volume of 450 cubic feet per ton and revenue of $79 per ton.

The freighter is divided into two cargo holds, starboard and port (right and left sides of the ship). The starboard hold has a volume of 14,000 cubic feet and a weight capacity of 26 tons. The port hold has a volume of 15,400 cubic feet and a weight capacity of 32 tons. For steering reasons, it is necessary that the weight be evenly distributed between the two sides of the freighter.

The owner may carry any combination of the two cargoes in the same hold without a problem. How should the freighter be loaded to maximize total revenue (how much of cargo A in starboard and port, and how much of cargo B in starboard and port, to maximize the value of what is carried)?

Bonus: How does the answer change if the engines and bridge, which together weigh 6 tons, are on the starboard side of the freighter, so the port side is usually loaded with 6 tons more cargo to equalize the weight?

Answer the questions in the given Word document: Chapter 2 and 3 Homework Questions.

Submit your answers in Excel, with each problem on a separate sheet.

Answers should be well-organized and labeled, and have objective functions and constraints set up in Solver.

Thank you guys!