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Department of Computing

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Department of Computing

    Department of Computing

    Goldsmiths College

    University of London

    CIS331: Introduction to Mathematical Modelling in Management Science

Lecturer: Prof. Robert Zimmer

Assignment 1: Sonoma Valley Wines (taken from Winston and Albright)

Date Due: 1 March

Submission: hand in on paper and electronically. Instructions to follow

Instruction:

    You are not required to answer all questions, but the more you answer the better. The

    assignment is worth 10% of the total marks for this course. You will be awarded

    points on the accuracy of your models and the completeness of your work. You must

    provide clear descriptions of how your models have been developed and where the

    numbers come from (as demonstrated in the book). ]

The Decision Scenario:

After graduating from business school, George Clark went to work for a Big Six accounting

    firm in San Francisco. Since his hobby has always been wine making, when he had the

    opportunity a few years 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 he has at the present. However, he figures that, if he persists, he will

    be able to leave accounting and live full-time from his winery 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 years, George is planning to start small.

    This is necessitated by both his lack of capital and his inexperience in wine making on a large

    scale, although he 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 he can live on weekends

    while he installs the irrigation systems and does the required work to the vines, such a pruning

    and fertilizing. To help maintain a positive cash flow during the first 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 on weekends

    during the spring-summer season.

    To being, George is going to use $10,000 in savings to finance the initial purchases 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 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 fist.

    Assignment 1: Sonoma Valley Wines Page 1 of 3

This way he will have a rough notion of the profitability and cash associated with his ideas

    before he develops a formal plan with proforma income statement and balance sheet. He has

    decided to make the preliminary planning horizon 2 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 how much he should allocate to purchasing

    grapes to make his favourite 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 $0.80 worth of grapes and each

    bottle of Sauvignon Blanc uses $0.70 worth of grapes. For the second year, the costs of the

    grapes per bottle are $0.75 and $0.80, 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 his Sauvignon Blanc’s price remains the same in both

    years at $7.00 a bottle.

    Besides the decision about the amounts of grapes purchased in the 2 years, George must make estimates of the sales level for the two wines during the 2 years. The local wine

    making association has told him that marketing is the key to success in any wine business;

    generally, demand is directly proportional to the amount of effort spent of marketing. Thus,

    since George cannot afford to do any marker research about sales levels due to his lack of

    capital, he is pondering how much money he should spend to promote each wine each year.

    The wine-making association has given him a rule of thumb that relates estimates 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 demand for six bottles will result. Similarly, for each dollar spent on adverting 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 year is available in the second year.

    A personal concern 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

    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 falls in the range between 40% and 70% of

    the overall number of bottles sold.

Assignment 1: Sonoma Valley Wines Page 2 of 3

    Questions:

1. 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. Develop a spreadsheet LP model to help him.

    2. Solve the linear programming model formulated in Question 1.

    3. After showing the business plan to the Bank of Sonoma, George learns that the loan

    officer is concerned about the market prices used in estimating the profits; recently is

    has been forecasted that Chile and Australia will be flooding the market with high-

    quality, low-priced white wines over the next couple of years. In particular, the loan

    officer estimates that the price used for Sauvignon Blanc in the second year is highly

    speculative and realistically might be only half the price George calculated. Thus, the

    bank is nervous about lending the money because of the big effect such a decrease in

    price might have on estimated profits. What do you think?

    4. Another comment the loan officer of the Bank of Sonoma has after reviewing the

    business plan is: I see that you do have an allowance in your calculations for the

    carryover of inventory of unsold wine from the first year to the second year, but you

    do not have any cost associated with this. All companies must charge something for

    holding inventory, so you should redo your plans to allow for this.” If the holding

    charges are $0.10 per bottle per year, how much, if any, does George’s plan change?

    5. The president of the local grape growers association mentions to George that there is

    likely to be a strike soon over the unionization of the grape workers (currently they are

    not represented be any union). This means that the costs of the grapes might go up by

    anywhere from 50% to 100%. How might this affect George’s plan?

    6. Before taking his business plan to the bank, George had it reviewed by colleague at

    the accounting firm where he works. Although his friend was excited about the plan

    and its prospects, he was dismayed to learn that George had not used present value in

    determining his profit. “George, you are an accountant and must know that money has

    a time value; and although you are only doing a 2-year planning problem, it still is

    important to calculate the present value profit.” George replies, “Yes, I know all about

    present value. For big investments over long time periods, it is important to consider.

    But in this case, for a small investment and only a 2-year time period, it really doesn’t

    matter.” Who is correct, George of his colleague? Why? Use an 8% discount factor in

    answering this question. Does the answer change if 6% or 10% discount rate is used?

    Use a spreadsheet to determine the coefficients of the objective function for the

    different discount rates.

    7. Suppose that the Bank of Sonoma is so excited about the prospects of George’s wine-

    growing business that they offer to lend him an extra $10,000 at their best small 1business rate -28% plus a %10 compensating balance. Should he accept the bank’s

    offer? Why or why not?

    8. Suppose that the rule thumb of George was given by the local wine-making

    association is incorrect. Assume that the number of bottles of Petite Sirah sold in the

    first and second year is at most four for each dollar spent on advertising. And likewise

    for Sauvignon Blanc, assume that it can be at most only five in years one and two.

    9. How much could profits be increased if George personal concerns (that Petite Sirah

    sales should account for between 40% and 70% of overall sales) are ignored?

     1 The compensating balance requirement means that only $9,000 of the $10,000 loan is available to George; the

    remaining $1,000 remains with the bank.

    Assignment 1: Sonoma Valley Wines Page 3 of 3

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