Question

You must SHOW ALL WORK ON NEXT PAGE to get credit and MUST ROUND to 2 decimal points (you can use back of page or below for calculations)! If you use a graphing calculator and simply write answers you will get ZERO CREDIT A company wants to maximize profits for two products: Green (earning $10 profit per unit) and Blue (earning $14 profit per unit). Machine Machine A B Green 3 3 Blue Total Available 2 120 1 90 To produce these items, the company uses time on Machines A and B and is limited to the total time each day as shown at the right. Additionally, the company must produce no less than 20 units TOTAL (if Green and Blue combined) each day to satisfy break even requirements and it cannot produce any more than 50 units of the Blue version each day What is the objective function equation/statement for this problem? (1 pt) 1. 2 What are the constraint equations for this problem? (2.5 pts) 3. Plotlabel the constraints on the graph attached and shade the feasible solution space. (8 pts) 4. Given your final graph below, What is the optimal quantity of the Green and Blue products & corresponding profit amount? (2 pts) Show proof that this is optimal profit (show all the other profits for possible combinations identified). (2.5 pts) Optimal Point/Profit Answer Proof Answers: 5. Which constraint(s) (if any) is/are binding? (1 pt) 6. Which constraintfs) (if any) is/are redundant? (1 pt) 7. How much slack or surplus do the constraints have (if any)? (2 pts) Graph increments are in units of 10. PLEASE graph X2 accordingly X WORKSPACE AS REQUIRED Feasible Points Workspace Plot Coordinates Workspace

Answer 1

Rest 4 Questons Dppade n its of yreen preducrd. 9nd Pints of Blue produds are Objechve statement of ths pro blem 1. 4sing maximize the profit of company dy Cimited time per day on machined maximi ze 10x,t 14K Constraind epuntring Graph 3. 3X,t 2-120 (a0,30 3x,+QX182o 60 2ne 20 3Xa=go OX,414 profit 20,30) at boo) profitz at l0,a0) ( 0,80) 200 profit (900) (30,0) at (0,60) profitz at (30,0) profit = 300 &40 a따 (ao,ao) Profit 2004 42o 2620 manimum prof+ whih is 840 (oJ'o)s