Linear Programming Applications

Table of Content

Instrument, located in Atlanta, Georgia, has two manufacturing plants. However, scheduling the workforce has been a challenge for Davis due to the fluctuations in product demand on a monthly basis. In order to address this issue, Davis recently started hiring temporary workers from Workers Unlimited, a specialized company that offers temporary employees to businesses in the greater Atlanta area. Workers Unlimited presented three contract options with varying lengths of employment and costs. The cost of the longer contract periods is higher because it is more difficult for Workers Unlimited to find temporary workers willing to commit to longer assignments. Davis anticipates the need for additional employees over the next 6 months, as outlined below.

Davis has the option to hire temporary employees each month. If, for example, Davis hires 5 employees in January under Option2, Workforce Unlimited will provide Davis with 5 temporary workers for 2 months: January and February. Davis will need to pay 5($4800)=$24000 for these workers. Due to ongoing merger negotiations, Davis wants to avoid any contractual obligations beyond June for temporary employees. Additionally, all temporary employees must undergo training as part of Davis’ quality control program, even if they have previously worked for Davis Instrument. The cost of training each temporary employee is estimated to be $875. Therefore, if a temporary employee is hired for one month, Davis incurs a training cost of $875, but incurs no additional training cost for employees on two- or three-month contracts. This information is presented in the Managerial Report.

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The report should include the following items for developing a model to determine the number of temporary employees Davis should hire each month under the contract plan in order to meet projected needs at a minimum total cost:

1. A schedule indicating the number of temporary employees that Davis should hire each month for each contract option.
2. A summary table displaying the number of temporary employees Davis should hire under each contract option, along with the associated contract cost and training cost for each option.
3. Summary totals outlining the total number of temporary employees hired, total contract costs, and total training costs.
Total number of temporary employees hired: 49
Total contract costs: $324,300
Total training costs: $42,875

3. If the cost to train each temporary employee can be reduced to $700 per month, what impact would this change have on the hiring plan? An explanation should be provided.
Furthermore, the implications of this change on the hiring plan for identifying methods to decrease training costs should also be discussed.

How much of a reduction in training cost would be required to change the hiring plan based on a training cost of $875 per temporary employee? The total training cost at $875 is $42875, while the total training cost at $700 will be $34300. Thus, there is a significant difference between the two. If the training fee decreases to $700, we will opt to hire more opt1 workers instead of opt3 workers due to their lower pay.

4. Suppose Davis hired 10 full-time employees at the beginning of January in order to fulfill part of the labor requirement over the next 6 months. If Davis can hire full-time employees for $16 per hour, including fringe benefits, what impact would this have on total labor and training costs over the 6-month period compared to hiring only temporary employees? Both full-time and temporary employees work approximately 160 hours per month. In total cost, when hiring full-time workers, it would amount to $158400, while when hiring temporary employees, it would be $324300 (Cost) + $42875 (Training). Therefore, hiring full-time employees is cheaper compared to hiring temporary employees.

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