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2.1 The Brown Furniture Company makes three kinds of office furniture: chairs, desks, and tables. Each product requires skilled labor in the parts fabrication department, unskilled labor in the assembly department, machining on some key pieces of equipment, and some wood as raw material. At current prices, the unit profit contribution for each product is known, and the company can sell everything it manufactures. The size of the workforce has been established, so the number of skilled and unskilled labor hours are known. The amount of wood, fabrication, assembly, and machining required for one unit of each product is known, and a known amount of wood can be obtained from the supplier each month. The managers would like to maximize their monthly profit. The data for this problem is given in the table below.     

Chairs Desks Tables Resource

Fabrication (hr) 4 6 2 2000hr

Assembly (hr) 3 8 6 2000hr

Machining (hr) 9 6 4 1440hr

Wood (sqft) 30 40 25 9600 sqft

profit/unit ($) 16 20 14

2.14 Coffee Blending and Sales Hill-O-Beans Coffee Company blends four component beans into three final blends of coffee: One is sold to luxury hotels, another to restaurants, and the third to supermarkets for store-label brands. The company has four reliable bean supplies: Argentine Abundo, Peruvian Colmado, Brazilian Maximo, and Chilean Saboro. The table below summarizes the very precise recipes for the final coffee blends, the cost and availability information for the four components, and the wholesale price per pound of the final blends. The percentages indicate the fraction of each component to be used in each blend.

Component Hotel Restaurant Market Cost per pound Pounds

Abundo 0.2 0.35 0.1 0.6 40000

Colmado 0.4 0.15 0.35 0.8 25000

Maximo 0.15 0.2 0.4 0.55 20000

Saboro 0.25 0.3 0.15 0.7 45000

Wholesale price

per pound 1.25 1.5 1.4

The processor’s plant can handle no more than 100,000 lb per week, and Hill-O-Beans would like to operate at capacity, if possible. Selling the final blends is not a problem, although the Marketing Department requires minimum production levels of 10,000, 25,000, and 30,000 lb, respectively, for the hotel, restaurant and market blends.

To maximize weekly profit, how many pounds of each component should be purchased?

How would the optimal profit change if there were a 1000-lb increase in the availability of Abundo beans? Colmado? Maximo? Saboro

How would the optimal profit change if there were a 1000-lb increase in the availability of Abundo beans? Colmado? Maximo? Saboro

Production Planning The Kim Camera Company produces four different camera models, known as C1–C4. Each model can be made by two different methods. The manual method requires work in the Fabrication, Assembly, and Test departments, while the automated method combines the Assembly and Test operations in one department. The first table below describes the price and cost features of the camera models, along with marketing information on the range of possible sales in the coming month. Because model C1 is delivered to one large retailer under a long-term contract, a threshold demand quantity of 1500 units must be met. For the other models, there is flexibility in how much demand to meet, up to a ceiling that represents maximum possible sales.

Open table as spreadsheet

C1 C2 C3 C4

125 175 200 135

Price 110 160 155 125

Manual cost 100 112 150 90

Auto cost 15 15 45 10

Manual margin 25 63 50 45

Auto margin 3000 2500 2000 3200

Sales max. 1500 0 0 0

Sales min.

The next table provides data on the various departments at the firm, consisting of the time per camera required in each department and the number of hours available in each department during the month.

Open table as spreadsheet

C1 C2 C3 C4 Hours

3 5 4 4 16000

Manual fab. 8 12 10 9 30000

Manual asy. 2 3 5 2 15000

Manual test 5 6 7 4 24000

Auto fab. 4 5 8 5 20000

Auto asy/test

What production plan will maximize profit for Kim Camera?

How would the solution in (a) change if there were no threshold requirement for Camera C1?