2. Our Last Device (OLD) needs to replace some of its aging equipment that produces molded frames for its best selling racing cycle. OLD can lease machines with a rated capacity of 2000 frames per month for $3,000 per month. Alternatively, OLD can pur- chase smaller machines with a rated capacity of 800 frames per month for $10,000 down and $1,000 per month. OLD has $50,000 available to purchase machines. OLD must produce 10,000 frames per month to keep up with demand. (a) Formulate a linear programming model to determine how many of each type of machine OLD should acquire so as to minimize total monthly payments. Make sure to define your variables and label your constraints. (b) Critique your model in part (a) against the four main assumptions of linear pro- gramming. (Remember, in a critique, you are analyzing the appropriateness of the model for the real world problem.) (c) Graphically solve the linear program you created in part (a). List the extreme points and their corresponding objective values. Describe the optimal solution in words. 2. Our Last Device (OLD) needs to replace some of its aging equipment that produces molded frames for its best selling racing cycle. OLD can lease machines with a rated capacity of 2000 frames per month for $3,000 per month. Alternatively, OLD can pur- chase smaller machines with a rated capacity of 800 frames per month for $10,000 down and $1,000 per month. OLD has $50,000 available to purchase machines. OLD must produce 10,000 frames per month to keep up with demand. (a) Formulate a linear programming model to determine how many of each type of machine OLD should acquire so as to minimize total monthly payments. Make sure to define your variables and label your constraints. (b) Critique your model in part (a) against the four main assumptions of linear pro- gramming. (Remember, in a critique, you are analyzing the appropriateness of the model for the real world problem.) (c) Graphically solve the linear program you created in part (a). List the extreme points and their corresponding objective values. Describe the optimal solution in words