Assignment:
A local party company manufactures New Year's Eve supplies. Specifically, they manufacture three types of noise makers: the siren, the horn and the trumpet. The required design time, manufacturing time and packaging time required for each noise maker and the total amount available to the company are given in the model below. The profit per noise maker is also given in the model.
Let S, H and T = the number of Siren, Horn and Trumpet noise makers produced, respectively.
Max Profit ($) = 3S + 4H + 2T
s.t.
S + 0.2H + 3T < 500 Design Hours
0.7S + H + 0.3T < 400 manufacturing hours
2S + 1.5H + 0.3T < 800 Packaging Hours
S, H, T > 0
Suppose that there are available up to an additional 20 hours of overtime for use in the manufacturing department and 50 hours for use in the design department. The overtime pay scale is $5 per hour more than the regular time rate that was used to determine the cost per noise makers for the manufacturing department and $7 more for the design department. However, we have the added restriction that combined you can only use at most 60 hours of overtime between the two departments.
Provide complete and step by step solution for the question and show calculations and use formulas.