Harold Grey owns a small farm in the Salinas Valley that grows apricots. The apricots are dried on the premises and sold to a number of large supermarket chains.Based on past experience and committed contracts, he estimates that sales over thenext five years in thousands of packages will be as follows:Forecasted DemandYear (thousands of packages)1 3002 1203 2004 1105 135Assume that each worker stays on the job for at least one year, and that Greycurrently has three workers on the payroll. He estimates that he will have 20,000packages on hand at the end of the current year. Assume that, on the average, eachworker is paid $25,000 per year and is responsible for producing 30,000 packages. Inventory costs have been estimated to be 4 cents per package per year, andshortages are not allowed.Based on the effort of interviewing and training new workers, Farmer Greyestimates that it costs $500 for each worker hired. Severance pay amounts to$1,000 per worker.a. Assuming that shortages are not allowed, determine the minimum constantworkforce that he will need over the next five years.b. Evaluate the cost of the plan found in part (a).c. Formulate this as a linear program.d. Solve the problem and round-off the solution and determine the cost of theresulting plan.
Harold Grey owns a small farm in the Salinas Valley that grows apricots. The apricots are dried on the premises and sold to a number of large supermarket chains.
Based on past experience and committed contracts, he estimates that sales over the
next five years in thousands of packages will be as follows:
Forecasted Demand
Year (thousands of packages)
1 300
2 120
3 200
4 110
5 135
Assume that each worker stays on the job for at least one year, and that Grey
currently has three workers on the payroll. He estimates that he will have 20,000
packages on hand at the end of the current year. Assume that, on the average, each
worker is paid $25,000 per year and is responsible for producing 30,000 packages. Inventory costs have been estimated to be 4 cents per package per year, and
shortages are not allowed.
Based on the effort of interviewing and training new workers, Farmer Grey
estimates that it costs $500 for each worker hired. Severance pay amounts to
$1,000 per worker.
a. Assuming that shortages are not allowed, determine the minimum constant
workforce that he will need over the next five years.
b. Evaluate the cost of the plan found in part (a).
c. Formulate this as a linear program.
d. Solve the problem and round-off the solution and determine the cost of the
resulting plan.
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