Industrial Chemicals produces two adhesives - Business Statistics

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Industrial Chemicals produces two adhesives used in the manufacturing process for airplanes. The two adhesives, which have different bonding strengths, require different amounts of production time: the IC-100 adhesive requires 20 minutes of production time per gallon of finished product, and the IC-200 adhesive uses 30 minutes of production time per gallon. Both products use 1 pound of a highly perishable resin for each gallon of finished product. Inventory currently holds 300 pounds of the resin, and more can be obtained if necessary. However, because of the limited shelf life of the material, any amount not used in the next two weeks will be discarded.

The firm has existing orders for 100 gallons of IC-100 and 120 gallons of IC-200. Under normal conditions, the production process operates eight hours per day, five days per week. Management wants to schedule production for the next two weeks to achieve the following goals:

Priority Level 1 Goals

Goal 1: Avoid underutilization of the production process.

Goal 2: Avoid overtime in excess of 20 hours for the two weeks.

Priority Level 2 Goals

Goal 3: Satisfy existing orders for the IC-100 adhesive; that is, produce at least 100 gallons of IC-100.

Goal 4: Satisfy existing orders for the IC-200 adhesive; that is, produce at least 120 gallons of IC-200.

Priority Level 3 Goal

Goal 5: Use all the available resin.

a. Formulate a goal programming model for the Industrial Chemicals problem. Assume that both priority level 1 goals and both priority level 2 goals are equally important.

b. Use the graphical goal programming procedure to develop a solution for the model formulated in part (a).

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Step 1 of 6

a)
Step 2 of 6

Write goal programming model.

Formulate the minimization function to achieve the goals.

Here, is priority level for goal 1, is the production of chemical less than the target value of goal 1, is the production of chemical greater than the target value of goal 2, is priority level for goal 2, is production of chemical less than the target value of goal 3, is production of chemical less than the target value of goal 4, is priority level for goal 3, and is production of chemical less than the target value of goal 5.
Step 3 of 6

The minimization function is subjected to following constraints.

Constraint for Goal 1:

The production process for both adhesives operates ,  therefore,

Here,  is number of gallons of IC-100 adhesive produced,  is number of gallons of IC-200 adhesive produced,  is the production of chemical greater than the target value of goal 1

Constraint for Goal 2:

Here,  is the production of chemical less than the target value of goal 2.

Constraint for Goal 3:

Here,  is the production of chemical greater than the target value of goal 3.
Step 4 of 6

Constraint for Goal 4:

Here, is the production of chemical greater than the target value of goal 4.

Constraint for Goal 5:

Here, is the production of chemical greater than the target value of goal 5.

Constraint for adhesives: increase or decrease the target values:
Step 5 of 6

b)

Show the calculation of graphical method as shown in Figure (1).

Figure (1) explains relationship between goal 1, goal 2, goal 3, goal 4, and goal 5.
Step 6 of 6

Show the graphical solution from Figure (1) as in Figure (2).

Therefore, the optimum amount of number of gallons of IC-100 adhesive produced is and the optimum amount of number of gallons of IC-200 adhesive produced is .