Reference no: EM132215912
1. Let A, B, and C be the amounts invested in companies A, B, and C. If no more than 50% of the total investment can be in company B, how can you express that as a constraint (Please show your work.)
a. 0.5A - 0.5B + 0.5C <= 0
b. - 0.5A + 0.5B - 0.5C <= 0
c. 0.5A - B - 0.5C <= 0
d. A - 0.5B + C <= 0
e. B <= 0.5
f. There is no solution
2. Which of the following combinations of constraints has no feasible region? (Please show your work.)
a. X + Y >= 10 and X - Y <= 5
b. X + Y >= 3 and X >= 7
c. X >= 5 and Y >= 15
d. X + Y >= 75 and X + Y <= 25
e. All of the above have a feasible region.
3. When building a chair, a carpenter uses 2 pounds of wood and 3 ounces of glue. If the Carpenter has 3 pounds of wood and 6 ounces of glue, how many chairs will he be able to build? (Please show your work.)
a. five chairs
b. four chairs
c. three chairs
d. two chairs
e. one chair
f. OTHER
4. Let Xi = 1 if Project i is selected, i = 1,2,3,4,5; and 0 otherwise:
Which answer below indicates that if Project 5 is selected, then Project 2 must also be selected?
a. X2 + X5 = 1
b. X5 - X2 <= 1
c. X2 + X5 <=1
d. X2 <= X5
e. X5 <= X2
5. Burglar John infiltrated a house. Unfortunately, he has a relatively small backpack which helps him to carry at most 30 lbs. Possessing a discriminating eye, he can immediately determine how much the items worth. There are 5 different items available. His aim is to maximize the dollar value of the stuff carried away, the overall weight being less than the weight he can carry by using his backpack. Weight and value of each item is given in the following table.
Item
Weight(lbs.)
Value($)
Available
1
10
5
1
2
25
15
1
3
13
12
1
4
45
45
1
5
19
20
1
What will be the first item the burglar should choose? (Please show your work by stating your reason.)
a. Item 1
b. Item 2
c. Item 3
d. Item 4
e. Item 5