1. Set up an initial simplex tableau, given the following two constraints and objective function: [13] Minimize Z=8X1+6X2 Subject to: 2X1+4X28 3X1+2X2X1,X260 2. Cars arrive at two drive-through windows at a post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. A single line would be formed and as a car reached the front of the line it would go to the next available clerk. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. Both clerks work at the same rate. Compute the probability that there are no cars in the system? [7] SECTION B [30] 3. A start-up company in Vanderbjilpark that produces toy buses and cars, has two primary resources available: injection moulding-machine time and assembly time. Over a week, the owner managed to schedule up to 38.77 minutes of work on the injection moulding-machine and up to 15.83 minutes of work on assembly. Each bus produced requires 8 minutes of injection moulding-machine time and 4 minutes of assembly time. Producing each car requires 6 minutes of injection moulding-machine time and 2 minutes of assembly time. The company's accounting department analyzes cost and sales figures and states that each bus produced will yield a R150 contribution to profit and that each car will yield a R90 contribution to profit. i. Formulate a linear programming model for this problem. [10] ii. Solve with the Simplex Method, using Excel Solver. [10] iii. Generate a sensitivity analysis report iv. What is the maximum amount of profit that the company can get by having some additional hours at the injection moulding-machine? v. What is the lowest number of hours allowable for assembly? [3] Totalmarks=50;Fullmarks=50 EBORE3A/EBONA3B GA 5 Assignment 2023-1 Page 3 of 5