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The Profit Function for Two Types of IPod Is =5x12+38x15x22+44x2+520 =-5 x_{1}^{2}+38 x_{1}-5 x_{2}^{2}+44 x_{2}+520

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The profit function for two types of iPod is :
Profit =5x12+38x15x22+44x2+520 =-5 x_{1}^{2}+38 x_{1}-5 x_{2}^{2}+44 x_{2}+520
where x₁ and x₂ represent number of units of production of basic and advanced iPods, respectively.
Production time required for the basic iPod is 6 hours per unit, and production time required for the advanced iPod is 8 hours per unit. Currently, 50 hours are available. The cost of hours is already factored into the profit function. a. Formulate an optimization problem that can be used to find the optimal production quantity of basic and advanced iPods.
b. Solve the optimization model you formulated in part a. How much should be produced?

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Definitions:

Process Losses

Reductions in team or organizational efficiency due to issues in group dynamics or operational inefficiencies.

Actual Group Performance

The real, observed output or results produced by a group when working on a task or project.

Sequential Assembly Line

A manufacturing process where a product is assembled in a fixed sequence of steps, with each workstation contributing a specific part of the assembly.

Conjunctive Task

A task in a group setting where the group's performance is determined by its weakest link or member, emphasizing the importance of each member's contribution.

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