*Please include Spreadsheets and formulas, if applicable*

1. Daves Sports Design (DSD) manufacturers a standard-size racket and an oversize racket. Each standard size racket uses .125 kilograms of a special graphite alloy, and each oversize racket uses .4 kilograms of the alloy. Over the next 2 weeks, 100 kilograms of the alloy will be available. Each standard size racquet uses 40 feet of string, while an oversize racket uses 45 feet of string. Over the next 2 weeks, 20,000 feet of string will be available. Each standard size racket takes 10 minutes to manufacture, while oversize rackets takes 12 minutes to manufacture. There are 80 hours of manufacturing time available over the next two weeks. Super Dave, the companys owner, requires that standard rackets make up at least 50% of the total weekly production. Each standard racket contributes $10 to profit, while oversize rackets contribute $15 to profit.

1. Write an LP model to find the optimal number of Standard and Oversize rackets to maximize profit.
2. Use Excel to find the optimal number of rackets. Write the solution and total profit earned below.

1. Suppose there were another 25 additional kilograms of graphite available. How much would profit change? Explain your calculations using the sensitivity report output.
2. Explain the Allowable Increase for the Time Constraint.
3. Explain why the Standard > 50% Constraint has a zero shadow price

A portion of the sensitivity report for the Dave's Sports Design problem is given below. Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$11 Graphite Constraint 12 100 40 $B$12 String Constraint 18720 0 20000 1E+30 1280 $B$13 Time Constraint 4800 0.85 4800 308.4337349 1800 $B$14 Standard > 50% Constraint 224 224 1E+30 100 60