1. Hontoy manufactures two economy cars designed for everyday use. Corius model has a more traditional engine designed for highway use. Micro model is slightly smaller designed for city driving. Hontoy manufactures engines for both the models in its Burlington, Ontario plant. Each Corius engine requires 3 hours of manufacturing time and each Micro model requires 7 hours of manufacturing time. The Burlington, Ontario plant has 2300 hours of engine manufacturing time available for the next production period. Hontoy's frame supplier can supply as many Corius frames as needed. However, the Micro frame is more complex and the supplier can only provide up to 290 Micro frames for the next production period. Final assembly and testing requires 4 hours for each Corius model and 2 hours for each Micro model. A maximum of 1000 hours of assembly and testing time are available for the next production period. The company's accounting department projects a prot contribution of $1800 for each Corius model manufactured and $2200 for each Micro model manufactured.

1. Formulate the linear programming model that can be used to determine the number of units of each model that should be produced in order to maximize the total contribution to prot.

2. Solve the problem graphically. What is the optimal solution?

3. Which constraints are binding?

2. Yorktown Inc, makes two dierent types of cricket bats. One bat for aggressive batting style and one bat for defensive batting style. The company has 900 hours of production time available in its wood cutting department, 300 hours available for nishing department, and 90 hours available in its packaging and shipping department. The production time requirements and the prot contribution per bat are given in the following table.

Production Time (hours)

Wood Cutting

Finishing

Packing And Shipping

Profit/Bat

Aggressive	2	1/3	1/5	$6
Defensive	1.2	1/2	1/9	$7

1. What is the linear programming model for this problem?

2. Find the optimal solution using the graphical solution procedure. How many bats of each model should Yorktown manufacture?

3. How many hours of production time will be scheduled in each department?

4. What is the slack time in each department?

3. Draw the feasible region for the problem and then and the optimal solution.

max 3A + 3B

subject to 2A + 4B 12

6A + 4B 24

A, B 0