Formulate an lp model for a minimum cost meal plan


Case Scenario:

Susan Cholette, campus dietitian for a small California college, is responsible for formulating a nutritious meal plan for students. For an evening meal, she feels that the following five meal-content requirements should be met:

i) between 900 and 1500 calories,
ii) at least 4 milligrams of iron,
iii) no more than 50 grams of fat,
iv) at least 26 grams of protein, and
v) no more than 50 grams of carbohydrates. On a particular day, Susan's food stock includes seven items that can be prepared and served for supper to meet these requirements. The cost per pound for each food item and its contribution to each of the five nutritional requirements are given in the accompanying table:

Formulate an LP model for a minimum cost meal plan that meets the given meal-content requirements.

Packaging:

In December 1998, Continental Packaging Division had been reorganized to facilitate a new strategy stressing market rather than product orientation. As the Packaging Division

Vice President told New England Business:

“We will start to look at our franchise not as the manufacture of blow-molded bottles, or two-piece aluminum cans, but as our relationship with the big package group marketers. Hitching Packaging’s wagon to big customers like General Foods makes more sense than latching on to a particular technology or shape or structure that will inevitably change. We do understand that such a relationship will require substantial capital expenditures every time a new packaging technology is demanded by our customers but we believe that the firm will generate cash flow adequate to the division needs.”

The new packaging organization operated in three major markets: Food and Beverage, Specialty Packaging, and International. Its cost reduction and productivity programs included closing a number of plants, which were unable to meet long-term profitability standards, while improving capacity utilization and line efficiencies at other facilities.  Basic research expenditures were reduced and emphasis directed towards business development and marketing. Continental Packaging had a major position in the fastest growing segment of the can industry the-two-piece aluminum can. However, both the short and long-term results of the packaging business would be determined by (1) the success of new product introductions, (2) continued emphasis on cost cutting even after demand reaccelerated, (3) whether or not metal cans would be besieged by another fundamental change in design and (4) the bargaining power of their customers. Those issues were very uncertain and hard to forecast especially given the strategic focus on a relatively few very large customers who would have substantial bargaining power.

The Outlook:

The packaging business was, in the main, an economically sensitive oligopolistic industry that mainly sold commodity products. It was very difficult to establish any kind of long-term competitive advantage other than cost and delivery reliability and other firms were positioned to do this as effectively as Continental. The firm’s decision to tie themselves to large customers while understandable and probably wise was likely to create serious pressures to reduce price and also make the packaging division less flexible because of the location decisions needed to cater to large customers.  The consultants did not believe that either sales growth or profitability would grow much faster than GDP in the future and felt that the cash needs of the division could be very high when the customers demanded new technology. Building the new technology into the plants would not reduce the push for lower prices by customers. The consultants felt that profitability would not increase over the next 10 years but would decline by about 50% and the Packaging Division’s cash flow would decline rapidly, from about $230,000,000 currently to zero by year five and be negative $100,000,000 in year 6 and get worse by about 20% per year thereafter. They forecast revenues to increase at the recent rate for the next decade. If the entire division were to be sold it would probably bring about $1,200,000,000 or about 70% of book value.
Some Financial Notes.

1. The firm’s debt is structured so that at least 40% of the net sale price of any assets must be paid to the debt holders.

2. In the most recent 4 years the corporate overhead costs have been about $200,000,000.

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Strategic Management: Formulate an lp model for a minimum cost meal plan
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