The profit function for two types of iPod is :
Profit $ =-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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The Answer of The profit function for two types of iPod is :
Profit $ =-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?

The Profit Function for Two Types of IPod Is =−5x12+38x1−5x22+44x2+520 =-5 x_{1}^{2}+38 x_{1}-5 x_{2}^{2}+44 x_{2}+520 =−5x12​+38x1​−5x22​+44x2​+520

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