Ames Manufacturing Plant produces two different replacement parts for dishwashers. During a normal shift, they have 7 hours of time available on their main fabrication machine. The machine will process 40 of Part X in an hour and 25 of Part Y. Each Part X requires .5 hours to assemble and each Part Y requires .4 hours. Ames has 64 hours if labor available on this line each shift. The painting booth can handle 40 parts per hour and can be used a max of 6 hours per shift. Ames has a $45 profit margin for Part X and $40 for Part Y. Below you can see the spreadsheet model with the optimal profit maximizing production plan and the sensitivity analysis. Answer the questions based on this output.

Time is in hours
Machining: Part X:.03 Part Y:.04. Available:7
Labor: Part X:.5 Part Y:.4 Available:64
Painting: Part X:.03 Part Y:.03 Available:6
Unit Profit: Part X:$45 Part Y:$40

Production Plan: Part X:0. Part Y:160

LHS RHS
Machining: 6.4 <= 7
Labor: 64<= 64
Painting: 4<= 6

Total Profit: 6400

Adjustable Cells

Cell. Name
$B$19 Production Plan Part X
Final Value: 0
Reduced Cost: -5
Objective Coefficient: 45
Allowable Increase: 5
Allowable Decrease: 1E+30

Cell: $C$10
Name: Production Plan Part Y
Final Value: 160
Reduced Cost: 0
Objective Coefficient: 40
Allowable Increase: 1E+30
Allowable Decrease: 4

Constraints

Cell: $B$13
Name: Machining LHS
Final Value: 6.4
Shadow Price: 0
Constraint RHS: 7
Allowable Increase: 1E+30
Allowable Decrease:.6

Cell: $B$14
Name: Labor LHS
Final Value:64

Shadow Price: 100

Constraint RHS: 64

Allowable Increase:6

Allowable Decrease: 64

Cell: $B$15

Name: Painting LHS

Final Value: 4

Shadow Price: 0

Constraint RHS: 6

Allowable Increase: 1E+30

Allowable Decrease: 2

A) What is the optimal solution?

B) What is the optimal value?

C) At what minimum Unit Profit would Ames consider manufacturing Part X?

D) The materials requirements for Part Y changed increasing its cost of production by $2 per unit. What impact will this have on the production plan and profit?

E) The materials requirements for Part Y changed increasing its cost of production by $5 per unit. What impact will Thai have on the production plan and profit?