Question $4$:

$($a$)$ Discuss in detail with examples what is meant by "Decision Support Framework". Use an example to illustrate your answer.

$($b$)$ 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 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.

task is to: