5. BiCycle, Inc, produces two models of a new line of lightweight bicycles, a deluxe and a professional model. Each deluxe model requires 3 pounds of a titanium alloy while the professional model requires 5 pounds. Since this alloy is in short supply, BiCycle can only get 600 pounds per month. In addition, management planning policies call for minimum sales goals of 25 units per month for the professional model, and also require that at least as many professional models as regular models must be sold. If Bicycle makes $40 profit for each deluxe model sold, and $50 for each professional model sold, what is the best product mix for the next month? The problem structure is shown below. (20 points) DECISION VARIABLES X = Number of deluxe models to produce X2 = Number of professional models to produce OBJECTIVE FUNCTION: (Maximize Profit) Max Z = 40 X + 50 X2 CONSTRAINTS (1) Titanium (2) Min Professional Models 3X15X2 600 X2 25 (3) Total number of clocks X1 - X2 0 (a) Solve using LINDO/LINGO. What are the values and interpretations of all slack and surplus variables, right hand side ranges, and shadow prices? (Attach your LINDO/LINGO output) (b) BiCycle can obtain additional alloy at a premium of $10 per pound for up to 100 additional pounds, and $15 per pound for additional alloy over 100 pounds. What should Bicycle do, why should they do it, and what is the impact on the objective function?