A linear programming computer package is needed.

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown.

Constraint	Television	Radio	Online
Audience per advertisement	300,000	54,000	120,000
Cost per advertisement	$2,000	$300	$600
Maximum media usage	10	20	10

To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.

(a)

If the promotional budget is limited to $20,500, how many commercial messages should be run on each medium to maximize total audience contact?

Television=

Radio=

Online=

What is the allocation of the budget among the three media, and what is the total audience reached?

Television Budget=

Radio Budget=

Online Budget=

Total Audience=

(b)

By how much would audience contact increase if an extra $100 were allocated to the promotional budget? (Round your answer to the nearest whole number.)

2.

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A linear programming computer package is needed.

The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows.

Type of Loan/Investment	Annual Rate of Return (%)
Automobile loans	9
Furniture loans	11
Other secured loans	12
Signature loans	13
Risk-free securities	10

The credit union will have $2,400,000 available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments.

• Risk-free securities may not exceed 30% of the total funds available for investment.
• Signature loans may not exceed 10% of the funds invested in all loans (automobile, furniture, other secured, and signature loans).
• Furniture loans plus other secured loans may not exceed the automobile loans.
• Other secured loans plus signature loans may not exceed the funds invested in risk-free securities.

How should the $2,400,000 be allocated to each of the loan/investment alternatives to maximize total annual return?

Automobile loans$=

Furniture loans$=

Other secured loans$=

Signature loans$=

Risk-free securities$=

What is the projected total annual return?

$

3.

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A linear programming computer package is needed.

Kilgore's Deli is a small delicatessen located near a major university. Kilgore does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.44, on one serving of Dial 911, $0.57. Each serving of Wimpy requires 0.25 pound of beef, 0.25 cup of onions, and 5 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.25 pound of beef, 0.4 cup of onions, 2 ounces of Kilgore's special sauce, and 5 ounces of hot sauce. Today, Kilgore has 18 pounds of beef, 13 cups of onions, 86 ounces of Kilgore's special sauce, and 58 ounces of hot sauce on hand.

(a)

Develop an LP model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today. (Let W = the number of servings of Wimpy to make and let D = the number of servings of Dial 911 to make.)

Max=

s.t.Beef=

Onions=

Special Sauce=

Hot Sauce=

W, D 0

(b)

Find an optimal solution. (Round your answers to two decimal places.)

(W, D) =

Profit = $

(c)

What is the dual value for special sauce? (Round your answer to two decimal places.)

$

Interpret the dual value.

For every 1 ounce increase in ---Select--- beef onions special sauce hot sauce , the profit will ---Select--- increase decrease by $ .

(d)

Increase the amount of special sauce available by 1 ounce and re-solve. (Round your answers to two decimal places.)

(W, D) =

Profit = $

Does the solution confirm the answer to part (c)?

YesNo

4.

[/0.5 Points]DETAILSASWMSCI15 4.E.011.

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A linear programming computer package is needed.

Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows.

Component	Supplier
	1	2	3
1	$11	$12	$13
2	$9	$10	$9

Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows.

Supplier	1	2	3
Capacity	700	1,100	900

If the Edwards production plan for the next period includes 1,100 units of component 1 and 900 units of component 2, what purchases do you recommend? That is, how many units of each component should be ordered from each supplier?

Component 1, Supplier 1 unitsComponent 1, Supplier 2 unitsComponent 1, Supplier 3 unitsComponent 2, Supplier 1 unitsComponent 2, Supplier 2 unitsComponent 2, Supplier 3 units

What is the total purchase cost (in $) for the components?