Suppose you are managing the production team for a large toy company that produces high quality figurines. There are two new toys that your company is considering for production – one is a regular version of an action figure, and the other is a collectible version that is much more detailed in its construction. The time it takes to produce a regular action figure is 20 person-minutes, while a collectible action figure requires 100 person-minutes. A regular action figure requires 40 grams of plastic, while a collectible action figure requires 60 grams. A total of 8000 person-minutes and 9000 grams of plastic are available each week. If you obtain a profit of $15 for each regular action figure, and $65 for each collectible action figure, how many of each product should be made each week in order to maximize profit? Keep in mind that your boss requires that at least 25 regular action figures and 30 collectible action figures be produced each week. To answer this question, follow the steps below:(a)Organize the above information using a mixture chart. Be sure to include the minimums!(b) Write down the resource constraint inequalities and the minimum inequalitiesPlastic inequality:Time inequality:Minimum inequality:(c) TRUE or FALSE: Producing 100 regular action figures and 70 collectible action figures is a feasible production policy.(d) TRUE or FALSE: Producing 20 regular action figures and 60 collectible action figures is a feasible production policy. (e) Write down a formula for the profit obtained by producing x regular action figures and y collectible action figures.(f ) Graph the feasible region for this mixture problem on the axes below. Be sure to clearly label all the corner points of the feasible region! Show your work!(g) Use the Corner Point Principle to determine the optimal production policy, and calculate the maximum possible profit. Show your work!
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