MGT 3410 Examination III Spring 2022
Answer all questions (take-home examination)
“I’ve neither given nor obtained Helpance on this examination.” _______ (scholar’s initials)
Do all the next issues.
I. Select the very best reply for every a number of selection. Please use CAPITAL letters to point your reply and write neatly. (20 factors)
1. ____ three.____ 5. ____ 7.____ 9. ____
2. ____ four.____ 6.____ eight.____ 10.____
1. Which of the next is a sound goal operate for a linear programming drawback?
A. Max 5xy
B. Min 4x + 3y + (2/three)z
C. Max 5×2 + 6y2
D. Min (x1 + x2)/x3
2. Which of the next statements is NOT true?
A. A possible answer satisfies all constraints.
B. An optimum answer satisfies all constraints.
C. An infeasible answer violates all constraints.
D. A possible answer level doesn’t should lie on the boundary of the possible area.
three. Innis Investments manages funds for quite a few corporations and rich purchasers. For a brand new shopper, Innis has been approved to take a position as much as $1.2 million in two funding funds: a inventory fund and a cash market fund. In accordance with Innis’s danger measurement system, every unit invested within the inventory fund has a danger index of eight, and every unit invested within the cash market fund has a danger index of three. Which is the target operate for this drawback?
A. Max 8S + 3M
B. Max 8S + 3M – 1.2X
C. Min 8S + 3M
D. Min 8S + 3M – 1.2X
four. An answer that satisfies all the constraints of a linear programming drawback besides the nonnegativity constraints is named
A. optimum.
B. possible.
C. infeasible.
D. semi-feasible.
5. Slack
A. is the distinction between the left and proper sides of a constraint.
B. is the quantity by which the left aspect of a ≤ constraint is smaller than the
proper aspect.
C. is the quantity by which the left aspect of a ≥ constraint is bigger than the
proper aspect.
D. exists for every variable in a linear programming drawback.
6. Given a linear programming mannequin:
Max 4×1 + 6×2
s.t. x1 + 2×2 < 6
2×1 + 4×2 < 18
x1, x2 > zero
Which of the next assertion is true?
A. The mannequin has just one optimum answer.
B. The mannequin has no possible options.
C. The mannequin has a number of optimum options.
D. The mannequin has unbounded answer.
7. A constraint that doesn’t have an effect on the possible area is a
A. non-negativity constraint.
B. redundant constraint.
C. normal constraint.
D. slack constraint.
eight. To seek out the optimum answer to a linear programming drawback utilizing the graphical technique
A. discover the possible level that’s the farthest away from the origin.
B. discover the possible level that’s on the highest location.
C. discover the possible level that’s closest to the origin.
D. Not one of the alternate options is appropriate.
9. Let xij = the manufacturing of product i in interval j. To specify that manufacturing of product 1 in interval three and in interval four differs by not more than 100 models, which of the next constraints are appropriate?
A. P13 – P14 < 100; P14 – P13 < 100
B. P13 – P14 < 100; P13 – P14 > 100
C. P13 – P14 < 100; P14 – P13 > 100
D. P13 – P14 > 100; P14 – P13 > 100
10. At any time when all the constraints in a linear program are expressed as equalities, the linear program is alleged to be written in
A. normal type.
B. bounded type.
C. possible type.
D. various type.
II. Downside Fixing
1. Think about the next linear programming drawback:
Min
s.t.
a. Write the issue in normal type. Determine slack/surplus variables. (10 factors)
b. The optimum answer of the above LP mannequin is (180/7, 150/7). What are the values of the slack and surplus variables on the optimum answer? (12 factors)
2. Think about the next linear programming drawback:
Max
s.t.
a. Determine the possible area. (12 factors)
b. Are any of the constraints redundant? If sure, then establish the constraint that’s
redundant. (10 factors)
c. Discover all the intense factors – checklist the worth of x1 and x2 at every excessive level. (6 factors)
d. What’s the optimum answer? (5 factors)
three. RVW (Restored Volkswagens) buys 15 used VW’s at every of two automobile auctions every week held at totally different areas. It then transports the vehicles to restore retailers it contracts with. When they’re restored to RVW’s specs, RVW sells 10 every to 3 totally different used automobile heaps. There are numerous prices related to the typical buy and transportation costs from every public sale to every restore store. Additionally there are transportation prices from the restore retailers to the used automobile heaps. RVW is worried with minimizing its complete value given the prices within the desk under.
a. Given the prices under, draw a community illustration for this drawback. (10 factors)
Restore Outlets Used Automotive Heaps
S1 S2 L1 L2 L3
Public sale 1 550 500 S1 250 300 500
Public sale 2 600 450 S2 350 650 450
b. Formulate this drawback as a linear programming mannequin. (15 factors)
(Be aware: You don’t want to unravel the mannequin.)
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Spring 2022 MGT 3410 Examination III
Answer all of the questions (take-home examination)
“I’ve neither given nor obtained help with this examination.” (Initials of the scholar)
Do all the next issues.
I. Select the very best reply for every a number of selection. Please use CAPITAL letters to point your reply and write neatly. (20 factors)
1. ____ three.____ 5. ____ 7.____ 9. ____ 2. ____ four.____ 6.____ eight.____ 10.____
1. Which of the next is a sound goal operate for a linear programming drawback?
A. Max 5xy
B. Min 4x + 3y + (2/three)z
C. Max 5×2 + 6y2
D. Min (x1 + x2)/x3
2. Which of the next statements is NOT true?
A. A possible answer satisfies all constraints.
B. An optimum answer satisfies all constraints.
C. An infeasible answer violates all
