MATH 156 Brookdale Community Find the Simplex Solver Solution Algebra Questions Help me out with a Simplex solver solution. MATH 156 Project 2 Sumer 2020 1

MATH 156 Brookdale Community Find the Simplex Solver Solution Algebra Questions Help me out with a Simplex solver solution. MATH 156
Project 2
Sumer 2020
1. Solve the following word problem. You should get infinite solutions. So find the pattern for
them and give a range of t values that is possible based on the word problem.
A trucking company plans on buying 4 kinds of trucks: a pick-up, a small flatbed, a large
flatbed, and a dump truck. The pick-up needs one worker to operate, 4 hours of maintenance and
3 hours of cleaning. The small flatbed needs one worker to operate, 1 hour of maintenance and
1 hour of cleaning. The large flatbed needs one worker to operate, 3 hours of maintenance and 2
hours of cleaning. The dump truck needs 2 workers to operate, 3 hours of maintenance and 2
hours of cleaning. If the company has exactly 46 workers, exactly 140 hours for maintenance
and exactly 112 hours for cleaning. How many of each kind of truck should they purchase?
2. The Kimble Firefighting Equipment Company makes alarm valves. It has two assembly
plants: Plant A in Atlanta and Plant B in Buffalo. All the alarm valves produced are shipped to
two warehouse locations, one in Pittsburgh and one in Savannah. The grid below shows the
distance between these locations:
Warehouse I: Pittsburgh
Warehouse II: Savannah
Plant A: Atlanta
685 miles
248 miles
Plant B: Buffalo
215 miles
907 miles
a. The current cost per mile for each alarm to ship is $0.03.. Calculate the total cost to produce
and ship an alarm valve from each location to each warehouse. Put your answers into a table like
the one above.
b. Plant A can produce at most 8000 alarm valves and Plant B can produce at most 10000 alarm
valves. The cost to produce an alarm valve is $12 at plant A and $18 at Plant B. If the current
weekly demand is for at least 9000 alarm valves to be shipped to Warehouse I and at least 6000
alarm valves to be shipped to Warehouse II.
(Hint: There should be 4 variables for example let x be the alarm valves produced in Atlanta and
housed in Pittsburgh, y be the alarm valves produced in Atlanta and housed in
Savannah……and so on.)
Write a linear programming problem to minimize the total cost of production and shipment for
the alarm valves made in each plant and housed in each warehouse. Define your variables, state
the objective function and list all constraints.
c. Solve the problem using the simplex solver. State your solution in a complete sentence. What
is the solution telling you?
d. In winter diesel gas prices increase, does your solution change if the price increased from
$0.03 per mile to $0.05 per mile? Rewrite your LP with these new costs and solve. What is the
impact on your weekly costs due to this price increase?
e. The plant in Buffalo is old and needs major renovations, while the plant in Atlanta is newer
and has room to expand. The company wants to look at the impact of shutting down the Buffalo
plant. Using the same costs from problem d. (with the higher gas prices). First expand the
capacity of the Atlanta plant from 8000 to 16000 and take the capacity of the Buffalo plant to 0.
Write the new LP and the optimal solution. What would be the cost of shutting down the Buffalo
plant? Would you recommend shutting down the Buffalo plant? Use your analysis to justify your
answer.

Purchase answer to see full
attachment