Question

1.

A corporation manufactures two variants of the same product: Deluxe (D) and Classic (C). The company has a limited amount of three ingredients used to manufacture these products: 4800 ounces of ingredient I; 9600 ounces of ingredient II and 2000 ounces of ingredient III. A box of Deluxe requires 2 ounces of ingredient I, 6 ounces of ingredient II and 1 ounce of ingredient III; while a box of Classic requires 3 ounces of ingredient I, 8 ounces of ingredient II and 2 ounces of ingredient III. Profits for a box of Deluxe are $0.40; and for a box of Classic $0.50. If the company manufactures 800 boxes of Deluxe and 600 boxes of Classic, which resource has “slack” (i.e., which resource is not fully used)?

	A.	Ingredient I and ingredient II
	B.	Ingredient II (only)
	C.	Ingredient I (only)
	D.	Ingredient I and ingredient III
	E.	Ingredient III (only)

2.

Suppose that two constraints of a linear program are 3X+Y ≤ 5000 and X+3Y ≤ 3000. The corner point representing the intersection of these two constraints is ...

	a.	impossible to determine uniquely.
	b.	none of the other answers.
	c.	Y is 0, X is 0.
	d.	Y is 1500, X is 500.

3.

A distributor packages and sells two types of products, A and B. The respective sales prices for the products are $10 and $5. The distributor has enough storage capacity for 1000 total products. The cost of storing the goods is $1 each. Packaging for product A requires 2 hours and for product B requires 5 hours. The packaging budget allows for only 5000 hours of labor for packaging. This linear program can be formulated as ...

	a.	Maximize 10A + 5B, such that, A >= 0, B >= 0, A + B <= 1000, and 2A + 5B <= 5000
	b.	Maximize 9A + 4B, such that, A >= 0, B >= 0, A + B <= 5000, 2A + 5B <= 1000
	c.	Maximize 9A + 4B, such that, A >= 0, B >= 0, A + B <= 1000, 2A + 5B <= 5000
	d.	Maximize 10A + 5B, such that, A + B <= 5000, and 2A + 5B <= 1000, and A >= 0, and B >= 0

4.

The three distinctive parts of a linear programming model formulation are the decision variables, the parameters and the model constraints.

True

False

Answer 1

Q1)

Deluxe = 800, Classic = 600

Ingredient I usage = 2*800+3*600 = 3400

4800 ounces of ingredient I are available. Only 3400 is used. Ingredient I is not fully used

Ingredient II usage = 6*800+8*600 = 9600

9600 ounces of ingredient II is available. Ingredient II is completely used.

Ingredient III usage = 1*800+2*600 = 2000

2000 ounces of ingredient III is available. Ingredient III is completely used.

C.	Ingredient I (only)