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# Hartley's furniture:Sensitivity analysis problem

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Solve linear programming problem. See the attached document for proper formatting.

Week 7

Hartley's makes furniture. The time required for each item is listed below.
Find the mix of products and sensitivity report to make the highest profit for Harley's.

Chairs Tables Bookcases Available
Assembly (minutes) 40 80 50 8100
Finishing (minutes) 20 30 30 4500
Wood (pounds) 10 80 50 9000
Unit profit \$125 \$360 \$300

a. If the profit per table increases by , will this change the optimal
production numbers? What can does the sensitivity report say about
changes in the total profit?

b. Suppose the profit per table increases by \$90 and the profit per
bookcase decreases by \$50. Will this change the optimal
production quantities? What can be said about the change in
total profit?

c. Suppose a worker calls in sick so 8 fewer hours are now
available in assembly. How much would this affect total profit?
Would it change the optimal production quantities?

d. Why is the shadow price for the wood constraint = 0?

e. If a new worker is hired to split their time between
assembly and finishing. What is the best way to split
the time or does it matter?