integer programming

After graduating from business school, George Clark went to work for a Big Six accounting firm in San Francisco. Since his bobby has always been wine making, when he had the opportunity a few yeas later he purchased 5 acres
plus an option to buy 35 additional acres of land in Sonoma Valley in Northern California.. He plans eventually to grow grapes on that land and make wine with them. George knows that this is a big undertaking and that it will require more capital than be has at the present. However, he figures that. If he persists he will be able to leave accounting and live full-time from his wine earnings by the time he is 40..
Since wine making is capital-intensive and since growing commercial ¬quality grapes with a full yield of 5 tons per acre takes at least 8 yeas. George is planning to start small. This is necessitated by both his 1ack of capital and inexperience in wine making on a 1arge scale, although be has long made wine at home. His plan is first to plant the grapes on his land to get the vines started. Then he needs to set up a small trailer where be can live on weekends while he installs the irrigation system and does the required work to get the vines started, such as pruning and feI1ilizing. To help maintain a positive cash flow during the first few years, he also plans to buy grapes from other nearby growers so he can make his own label wine. He proposes to market it through a small tasting room that he will build on his land 'and keep open on weekends during the spring-summer season.
To begin, George is going to use $10,000 in savings to finance the initial purchase of grapes from which he will make his first batch of wine. He is also thinking about going to the Bank of Sonoma and asking for a loan. He knows that, if he goes to the bank, the loan officer will ask for a business plan; so he is trying to pull together some numbers for himself first. This way he will have a rough notion of the profitability and cash flows associated with his ideas before he develops a formal plan with a pro forma income statement and balance sheet. He has decided to make the preliminary planning horizon two years and would like to estimate the profit over that period. His most immediate task is to decide how much of the $10.000 should be allocated to purchasing grapes for the first year and how much to purchasing grapes for the second year. In addition, each year he must decide bow much be should allocate to purchasing grapes to make his favorite Petite Sirah and how much to purchasing grapes to make the more popular Sauvignon Blanc that seems to have been capturing the attention of a wider market during the last few years in California.
In the first year each bottle of Petite Sirah requires $.80 worth of grapes and, each bottle of Sauvignon Blanc uses $.70 worth of grapes. For the second year, the costs of the grapes per bottle are $.75 and $.85. respectively.
George anticipates that his Petite Sirah will sell for $8.00 a bottle in the first year and for $8.25 in the second year, while the Sauvignon Blanc's price remains the same in both years at $7.00 a bottle.
Besides the decisions about the amounts of grapes purchased in the 2 years, George must make estimates of the sales level for the two wines during the two years. The local wine making association has told George that marketing is the key to success in any wine business; generally, demand is directly proportional to the amount of effort spent on marketing. Thus, since George cannot afford to do any market research about sales levels due to his lack of capital, he is pondering bow much money he should spend to promote each wine each year. The wine making association bas given him a role of thumb that relates estimated demand to the amount of money spent on advertising. For instance, they estimate that for each dollar spent in the first year promoting the Petite Sirah a demand for five bottles will be created and for each dol1ar spent in the second year, a demand for six bottles will result. Similarly, for each dollar spent on advertising for the Sauvignon Blanc in the first year, up to eight bottles can be sold; and for each dollar- spent in the second year, up to ten bottles can be sold.
The initial funds for the advertising will come from the $10,000 savings. Assume that the cash earned from wine sales in the first is available in the second year for purchase of grapes and advertising.
A personal concern that George has is that he maintain a proper balance of wine products so that he will be well positioned to expand his marketing capabilities when he moves to the winery and makes it his full time job. Thus, in his mind it is important to ensure that the number of bottles of Petite Sirah sold each year range between 40% and 70% of the overall number of bottles sold.

Questions: George needs help to decide how many grapes to buy, how much money to spend on advertising, how many bottles of wine to sell and how much profit he can expect to earn over the two year period. Formulate a model (using integer programming) and solve to address these issues.