Harold Grey owns a small farm in the Salinas Valley that grows apricots. The apr

Question

Harold Grey owns a small farm in the Salinas Valley that grows apricots. The apricots ate dried on the premises and sold to a number of large supermarket chains Based on past experience and commuted contracts, he estimates that sales over the next five years in thousands of packages will be as follows. 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. Assuming that shortages are not allowed, determine the minimum constant workforce that he will need over the next five years. Evaluate the cost of the plan found in part. Formulate this as a linear program. Solve the problem and round-off the solution and determine the cost of the resulting plan.

Explanation / Answer

Answer:a The first step is to determine how productive one worker is; but since every unit is in years, this is pretty much done. So, the next step is look at the cumulative demand compared to cumulative production (be consistent with the units… one employee can produce 30 packages per year (in thousands)).

However, in building the table, notice that we’re starting with 20 (thousand) in inventory already. So that first year, we only need to produce 300 – 20 = 280 packages. The following table shows the ratios:

Based on this, we would need 9.33 (or rounded up, 10) employees for the whole 5 years; considering that he already has 3 workers, he would need to hire 7 more.

Notice that the ending inventory continues to grow and never decreases. If you look at the forecasts, the highest demand is in the first year and so the number of employees is set to meet that demand. Plus, rounding up to 10 employees further increases this gap. If you play with the data, you would see that having 9.33 employees would decrease that final ending inventory by 100.

If the idea is to have the same quantity of employees every year, we could look at maybe only 9 employees (or even less) over the 5 years. However, this would result in not enough packages being produced in that first year (and the problem statement allows for no shortages).

Answer:b

Year Forecasted demand Cumulative demand Cumulative production Employees needed 1 280 280 30 9.33 2 120 400 60 6.67 3 200 600 90 6.67 4 110 710 120 5.92 5 135 845 150 5.63

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