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, 60 hours are available. The cost of hours is already factored into the profit function. Formulate an optimization problem that can be used to find the optimal production quantity of basic and advanced iPods. Solve the optimization model you formulated, what is the optimal value of the objective function? Round your answer to one decimal place.

The number of basic units is 3 and the number of advanced unit is 4.

Explanation:

Optimization function is a real valued function that is either minimized or maximized relative to the given set of feasible variables. Therefore if our maximum value for the production of both types of Ipod is 50 hours and if it takes 6 hours to produce basic Ipod and 8 hours to produce advanced Ipod than optimization model is expressed as 6*x + 8 * y = 50. From this we have a set of possible solutions.

If x = 0 than y = 6, 2 it is not possible since it is not the natural number.

If y = 0 than x = 3, 57, it is not a natural number.

The only solution that satisfy the above condition is when x = 3 and y = 4.