A Company produces two products. Relevant information for eachproduct is shown in the Table below. The company has a goal of $48in profits and incurs $1 penalty for each dollar it falls short ofthis goal. A total of 32 hours of labor are available. A $2 penaltyis incurred for each hour of overtime (labor over 32 hours) used,and $1 penalty is incurred for each hour of available labor that isunused. Marketing considerations require at least 5 units ofproduct 1 and 10 units of product 2 be produced. For each unit ofeither product by which production falls short of demand, a penaltyof $5 is assessed.
Product 1 - Product 2
Labor Required - 4 hours - 2 hours
Contribution to profit - $4 - $2
1. Formulate a weighted goal programming that can be used tominimize the penalty incurred by the company. Do NOT solve, justformulate.
2. Suppose that company sets (in order of importance) the followinggoals:
a. Goal 1: Avoid underutilization of labor
b. Goal 2: Meet demand for product 1
c. Goal 3: Meet demand for product 2
d. Goal 4: Do not use overtime
Formulate and solve the preemptive goal programming model for thissituation using Excel solver. Describe clearly the optimal solutionto this problem using a managerial statement.
