### Manufacturer produces two different types of tennis balls

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1. ServKing is a tennis equipment manufacturer produces two different types of tennis balls, the SpinTec and the CourtMinder. The tennis balls are manufactured in batches; each batch of the SpinTec yields \$14 profit, while each batch of the CourtMinder yields \$7 profit. The maximum daily demand is for 150 batches of each type. The tennis balls are made using three separate processes: making the core, adding the middle layer, and coating with felt. There is one machine for making the core and one for adding the middle layer; three machines are available for the coating process. Both types require 3 minutes per batch to make the core. Adding the middle layer takes 6 minutes per batch for the SpinTec, but only 2 minutes per batch for the CourtMinder. The felt coating process takes 15 minutes per batch of SpinTec and 9 minutes per batch of CourtMinder. Each machine can be operated for 10 hours per day. Formulate a linear programming model to determine the optimal number of batches of each type of tennis ball that ServKing should produce, with the goal of maximizing profit. Use either the graphical or algebraic solution method to determine this optimal solution and the associated profit.

2. As part of a quality improvement initiative, employees of MindWorks must complete a three-day training program on teaming and a two-day training program on problem solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem solving be offered during the next six months. In addition, senior management has specified that at least 25 total training programs must be offered during this period. The consultant that teaches these training programs has 84 available days of training time. Mindworks pays the consultant \$2,500 for each program on teaming and \$2,000 for each program on problem solving. Develop a linear programming model that can be used to find the number of each type of training program that should be offered in order to minimize total cost. Solve for the minimal cost solution using either the graphical or algebraic method, and determine the associated cost.

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