In Homework #1 and #2 you organized and solved a 2-variable LP to help decide ho

Question

In Homework #1 and #2 you organized and solved a 2-variable LP to help decide how much of each asphalt mix (airport and residential) to produce. You have successfully negotiated a newer, larger contract that includes two new mix types: an interstate mix for the department of transportation and an experimental mix for a local research lab. You are contracted to produce at least 8 tons of airport mix, 20 tons of interstate mix, 4 tons of experimental mix and 13 tons of residential mix per day. To accommodate these new mixes you have increased your plant capacity to 50 tons/day and arranged to have 925 total units of binder available and 325 total units of polymer available to meet your daily demand. Additional problem data is shown in the table below. Using this new data, revise your LP accordingly and do the following. a. Create a new "expanded version" of the Asphalt Mix Lp that includes the new mix types. b. Solve the LP using the Simplex Method (include a tableau for each pivot, be sure to report your final solution.)

Explanation / Answer

Let the total quantity of airport mix be a tons
total quantity of interstate mix be I tons
total quantity of experimental mix be e tons
total quantity of residential mix be r tons

Let z be the total profit

Objective function:
Maximise z = 85a + 80i + 50e + 30r

Subject to constraints:
a) Total capacity of plant is 50:
a + i + e + r <= 50

b) Availability of binder
23a + 20i + 18e + 12r <= 925

c) Availability of polymer
9a + 7i + 12e + 2r <= 325

d) Minimum quantity to be produced
a >= 8
i >= 20
e >= 4
r >= 13

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