QBUS2310 Practice Midsemester Exam Semester 1, 2022
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QBUS2310 Practice Midsemester Exam
Semester 1, 2022
max
z s.t.
min(x1 , x2 , x3 }
max(|x1 - x2 |, |x2 + x3 |, |x3 - x1 | - min(x2 , x3 }} s min(x1 + x2 , x3 - |x2 |} x3 > 1 + x2
x1 , x2 , x3 > 0.
min
z s.t.
6x1 - 6x2 - 3x4
-5x1 + 7x2 - 7x3 - 2x4 =
2x1 - x2 - 4x3 + 2x4 =
7x1 - 5x2 + 4x3 + 4x4 =
-6x1 - 4x2 - 2x3 + 6x4 s
x1 > 0, x2 free, x3 s 0, x4 free.
1
-4
4
-3
3. (10 points) Consider the following LP:
min x1 + 4x2
z
s.t. 2x1 + 3x2 > -1
9x1 + 5x2 s 3
x1 s 0, x2 s 0.
Using complementary slackness, verify whether x = 、0, - 
← is optimal or not.
4. (20 points) Top Brass Trophy Company makes large championship trophies for youth sports leagues. At the moment, they are planning production for semester 1 sports: basketball and rugby. Each type of trophy has a wood base and an engraved plaque. The amount of wood require, profit per trophy and total demand for semester 1 differs by the type of trophy. These numbers are given in the following table:
rugby
plaques required per trophy
wood required per trophy
profit per trophy
demand
Furthermore, we know that 1450 plaques and 450m of wood are available in total. Every trophy of unmet demand requires you to pay a penalty of ✩2. Unsold trophies must go into storage at a cost of ✩1 per trophy. Formulate an LP to find the production plan that maximizes the amount you earn.
2022-04-09