Question

Please show in excel with equations! 1) A Chemical company manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes: 1 and 2. Running process 1 for an hour costs $400 and yields 300 units of A, 100 unit of B, and 100 unit of C. Running process 2 for an hour costs $100 and yields 100 unit of A and 100 unit of B. To meet customer demands, at least 1000 units of A, 500 units of B, and 300 units of C must be produced daily. [Chapter 3]

a. Write the algebraic formulation for the problem.

b. Use Solver to determine a daily production plan that minimizes the cost of meeting company’s daily demands.

c. Confirm graphically that the daily production plan from part a minimizes the cost of meeting company’s daily demands.

d. What happens to the decision variables and the total cost when the hourly processing cost for process 2 increases by 50$. How large must this cost increase be before the decision variables change? What happens when it continues to increase beyond this point? [hint: use sensitivity report]

e. What are the values of slack and surplus for constraints? [hint: use solver report] f. Which constraints have non-zero shadow prices? Explain.

Answer 1

Three types of chemicals are produced A,B and C. Also.there are two types of processes (machines) available for production.

Decision Variables:X1=Number of hours of process 1 used
X2=Number of hours of process 2 used

Constraints:For chemical A: 3X1+X2+X3> 10

For chemical B: X1+X2> 5
For chemical C: X1> 3

Objective function:

Z=Cost of meeting daily demands for chemicals=Cost of operating process 1 and 2

Minimize Z= 4X1=X2

Point'	X1	X2	Z
A	5	0	4*5+0=20
B	3	2	4*3+2= 14

Point B is the optimal point. Processes 1 and 2 should be used

3 hours and 2 hours, respectively