Decision Variables DV#1 DV#2

Objective Function Coefficient

Constraints: LHS Sign RHS

Constraint #1

Constraint #2

Constraint #3

Constraint #4

5.1 gear manufacturer is planning next week's production for four types of gears. Because there are

limited resources in the plant for production, the manufacturer can outsource the gears by purchasing

these gears from a regional supplier. The regional supplier can supply a maximum of 300 units of each type of gear

(Hint: this is 4 constraints). The table below shows the exact demand for the gears, the revenue per unit, and the outsource cost per unit if the gears are purchased from the supplier. The

manufacturer generates the same revenue per unit for the gears regardless of whether the gear is manufactured in their plant and then sold to their customers or outsourced from their supplier and then sold to their customers.

PRODUCT

GEAR TYPE GEAR A GEAR B GEAR GEAR D

Demand 650,500450,550

REVENUE16.75,17.50,19.90, 21.50

OUTSOURCE COST 15.50,15.00,16.50,16.50

When the gears are manufactured in the own plant, the gears must be processed through three

different departments: forming, hardening, and deburring. The table below shows the processing time (in hours) for each type of gear in the departments as well as the capacity for each department and the cost per hour for processing the gears in those departments.

The cost per hour for processing the gears is provided so that you can calculate the manufacturing cost.

PROCESS

GEAR A(hrs./unit) GEAR B (hrs./unit)GEAR C(hrs./unit) GEAR D (hrs./unit) DEPARTMENTCAPACITY (hours) COST($/hr.)

FORMING .57,.63,.59,.72,900, 9.75

HARDENING .50,.45,.51.60,900,8.60

DEBURRING .60, .57, .62,.35,900,9.25

Formulate and solve this problem in Excel to determine the production and/or outsource plan which will

meet the requirements and maximize the profit. (Hint: processing costs in the second table effect only the

profit for the gears that are manufactured and not the gears that are outsourced)

SOLUTION: The optimal solution, the value of the profit, should be $6,498.23($10 for rounding). Some of your decision variables will not be integers. The profit to make one Gear A in house and sell it to your customer is $1.34.

The profit to buy one Gear A from your supplier and sell it to your customer is $1.25.

Formulation: Formulate this problem by defining decision variables, objective function, and constraints in standard format.

Questions:

a)If you could add 10 hours of capacity to any department to increase profit -adding one hour of

capacity to which department would generate the biggest increase in profit: Forming, Hardening, or Deburring? Explain.

b)Which of the following constraints have slack-Forming, Hardening, or Deburring? Explain.

c)In your solution, how many Gear C's should the company make?

d)If the cost per hour of the hardening process increases to $12/hr. -how many Gear A's should the company make with this new process cost?