Question

A furniture factory produces two types of desks. Type I and type II, in the cutting and assembly departments. the number of hours available in each department is: in department A 624 hours and in department B it is a third (1/3) more hours than in department A. To manufacture a type I desk unit it takes 3 hours in department A and 8 hours in department B. To manufacture a type II desk unit, 10 hours are required in department A and 5 hours in department B. If the utility for each type II desktop is $ 500,000.00 and the utility of the desk Type I is 20% less than Type II. How many units of each type of desk should be manufactured to MAXIMIZE utility? Find the feasibility intervals for R1 and R2

Answer 1

HI,

Please find the answer as below.

I have used excel solver to solve the problem. I have attached the screenshot of Input Data, Formulas and Constraints used along with the optimal solution, sensitivity report.

Furniture factory need to produce 78 units of Type I desks and 39 units of Type II desks which will give maximum utlity of $ 5,07,00,000.

1. Snapshot of Input Data

2. Snapshot of Formulas Used

3. Snapshot of Constraints Used

4. Snapshot of Optimal Solution

5. Snapshot of Sensitivity report and Limit Report

To get the sensitivity report, we need to remove the integer constraint.

For Coefficients

Feasibility interval for R1 is - (4,00,000-250000) to ( 400000+400000) which is 150000 to 800000.

Feasibility interval for R2 is - (5,00,000-250000) to ( 400000+833333.33) which is 250000 to 1233333.33.

For Constraints

Feasibility interval for C1 is - (624-312) to ( 624 + 1040 ) which is 312 to 1664.

Feasibility interval for C2 is - (832-520) to ( 832+832) which is 312 to 1664.

Limit Report