For this reason the firm sets periodic quotas only for the seven salespersons. The firm sells nine product lines, listed in Table A, where each column shows how $1 in sales in each of the seven territories is distributed among various products. For example, the .07 coefficient for the first product, belts, indicates that on average, 7cents of every dollars worth of merchandise sold in the territory 1 is generated by belts. These distributions were found to be quite stable over time, regardless of the size of the account.

The market potential of each sales territory for the next planning period is presented in Table B. This is JVHs estimate of potential demand for its products next year for each of the seven territories at the present level of advertising. These demand forecast were based on past sales records, information gathered from trade associations, and governmental agencies, as well as independent forecast made by consulting firms that specialize in economic analysis of trade areas.

The cost of a dollars worth of merchandise required in the production of each product line, together with the corresponding sales commissions paid on each dollar of sales, is depicted in Table C. The production capacity of the nine production lines is given in Table D.

During recent years, the companys sales and profits have been growing very slowly. Last year, the company netted about $200,000 on sales of $650,000. Mr. White, the president of JVH Jewelry, was not pleased with the results. White felt there was a large quantity of unutilized production capacity as well as market potential. Mrs. Garp, the vice president of marketing, disagreed with Mr. Whites assessment. She felt that the company was at or near optimal operating conditions and that very little could be done within the framework of the existing conditions.

Last Monday, the president called the executive management team together and requested proposals for improving the situation. Mrs. Garp suggested an increase in the marketing efforts, especially in territories 2, 4, and 6, where current market potential is lowest. The VP for production suggested increasing production of those product lines that yield the highest return. The controller suggested dropping the least profitable products or territories, or both. The president was reluctant to accept any of these suggestions, because both the market potential and the production capacity were underutilized. Furthermore, the specific marketing plan proposed violated the production capabilities, and the proposed increase in certain product lines violated the marketing capabilities.

The president finally decided to call you in because of your background in quantitative analysis particularly linear programing. He wants you to prepare a report which is to include the following items:

1. Evaluate the existing situation: determine if the company is indeed close to optimal operating conditions.
2. Analyze the marketing and production proposals presented by the VPs and the controller.
3. If possible submit other proposals; determine their feasibility and profitability.
4. Analyze the pricing and commission policies; submit recommendations.

Table A Dollar value of sales for nine Products in Seven Territories

		Sales Territory
Product Line		1	2	3	4	5	6	7
1	Belts	0.07	0.02	0.01	0.15	0.18	0.15	0.00
2	Buckles	0.05	0.00	0.00	0.10	0.10	0.07	0.00
3	Packaged Goods	0.20	0.35	0.30	0.25	0.25	0.25	0.50
4	Necklaces	0.07	0.07	0.07	0.10	0.15	0.10	0.03
5	Earrings	0.15	0.15	0.15	0.15	0.15	0.15	0.15
6	Bracelets	0.10	0.20	0.10	0.10	0.10	0.10	0.05
7	Gold stone	0.18	0.10	0.17	0.10	0.05	0.05	0.12
8	Hematite	0.15	0.08	0.17	0.02	0.02	0.10	0.12
9	Job Turquoise	0.03	0.03	0.03	0.03	0.00	0.03	0.03
Total		1.00	1.00	1.00	1.00	1.00	1.00	1.00

Table B JVHs Market Potential in Each of Seven Selling Areas

Sales territory	Market Potential (Maximum)
1	$ 225,000
2	135,000
3	150,000
4	100,000
5	210,000
6	80,000
7	250,000
Total	$1,150,000

Table C Material Cost and Sales Commissions for the Nine Product Lines

Product Line	Cost of $1 in Merchandise	Sales Commissions on $1 in Merchandise
1-6 inclusive	$ 0.50	$ 0.15
7-9 inclusive	0.67	0.10

Table D Product Line Capacity

Product Line	Product Line Capacity
1	70,000
2	20,000
3	210,000
4	70,000
5	150,000
6	100,000
7	150,000
8	150,000
9	30,000

Regarding the Constraints:

1. Production line capacity given in Table D. The capacity for each product line is allocated according to the percent of each dollars sale found in Table A
2. Table B gives the market potential for each territory.
3. Therefore the constraints must account for all of the product lines and all of the territories.

Regarding the objective function:

1. Table C provides you with variable cost for the products. These variable cost are given in two tiers. (remember fixed and variable cost from accounting)
2. Also remember what a contribution margin is. (selling price variable cost = contribution margin)
3. This means that each tier will have its own variable cost and therefore its own contribution margin.
4. The contribution margins will factor into the objective function coefficients.