An electronics company produces two types of television sets, color and black-and-white.  The production of a color set requires 10 hours of skilled and 100 hours of unskilled labor.  The production of a black-and-white set requires 5 hours of skilled and 150 hours of unskilled labor.  The company has 100 hours of skilled labor and 1,500 hours of unskilled labor normally available per month for the production of television sets.  The maximum number black-and-white and color sets that can be sold each month are 45 and 70, respectively.  The profit margin from the sale of a color set is $20, whereas it is $15 from a black-and-white set.  The company has set the following goals:

1. Avoid the over utilization of skilled labor since it is hard to obtain in the labor market.
2. Minimize the under utilization of unskilled labor.
3. Meet the demand as much as possible.
4. Limit over utilization of unskilled labor to 100 hours.

2)

A department store plans to schedule its annual advertising.  The total budget is set at $200,000.  The store can purchase local radio spots at $100 per spot, local television spots at $500 per spot and local newspaper advertising at $200 per ad.  The payoff from each advertising medium is a function of its audience size and audience characteristics.  The generally accepted objective criterion for advertising is audience points, reflected in the following table:

The president of the firm has established the following goals for the campaign:

1. The total budget should not exceed $200,000.
2. Meet the contract with the local television station that requires that the firm spend at least $30,000.
3. The corporate advertising policy prohibits annual newspaper ad expenditures in excess of $50,000.
4. Maximize the audience points for the advertising campaign.

3)

The Midtown City Council is reviewing housing proposals for a new development area.  There is some dispute among various interest groups as to what goals should be sought.  The zoning committee has recommended three types of housing:  one-family houses, deluxe condominiums and apartments.  The zoning committee has compiled the following data for each type of housing:

There are 50 acres available for zoning.  The League for Better Housing has conducted a campaign to gain housing for at least 500 families.  The Taxpayers’ Uniion has strongly lobbied for an added tax base of $5,000,000.  The Gray Panthers have disrupted the city council meetings to demand that taxes for city services be no more than $250,000.  The city council hired a public opinion survey company to assess the priorities of the citizens.  The poll results are as follows:

 Based on this survey the city council has established the following goals:

1. Provide housing for at least 500 families.
2. Establish at least $5,000,000 worth of new tax base.
3. Limit taxes for city services to $250,000.
4. Reserve at least 5 acres for a neighborhood park area.

4)

Acme Sawmill can produce plywood, chipboard and pulp for sale, realizing profit margins of $10, $9 and $6 per ton, respectively.  The mill can run any number of operations at the same time, but the setup costs for each of the operations differ.  While the pulp production only costs $2,000 to set up the plywood production costs $50,000 and the chipboard production costs $25,000.  Plywood consists of 95% wood and 5% resin glue.  Chipboard consists of 91% wood, 5% resin glue and 4% other additives.  Pulp consists of 86% wood and 14% other additives.  Demand limits the amount of plywood produced to 10,000 tons, while as much as 5,000 tons each may be produced of chipboard and pulp.  For the next month of production there are 15,000 tons of wood and 500 tons each of resin glue and other additives available.   Finally, Acme’s customers always place orders for whole tons of plywood and chipboard.  No partial tons may be accepted.

The operations manager at Acme has set the following goals for the upcoming month:

1. Achieve at least $70,000 profit.
2. Avoid having to special order more glue and additives.