Math 1

MATH451-X Data Driven Decision Making (Full Intellipath)

Transportation

Helen’s transportation company tries to deliver the following crops. There are a total of 600 boxes of apples, 500 boxes of bananas, 450 boxes of nectarines, and 350 boxes of peaches. These equal sized boxes can carry up to 25 pounds of apples, 35 pounds of bananas, 45 pounds of nectarines, and 30 pounds of peaches. The shipping charge for apples, bananas, nectarines, and peaches are $6.35, $6.45, $6.35, and $6.50 per box, respectively. The truck has a weight limit of 40,000 pounds and a capacity not more than 1,200 boxes.

Question 1

How many boxes of nectarines did she deliver after running the problem through Excel’s Solver?

450

0

350

500

Question 2

How much is the weight of the crops as the truck is completely loaded and ready to move?

38,800 pounds

36,750 pounds

40,000 pounds

1,200 pounds

Question 3

What is the smallest coefficient the shipping charge per box of nectarines can be changed to in order for her to deliver part or all of the nectarines after running the problem through Excel’s Solver?

$6.50

$7.00

$7.36

$7.50

Question 4

Your shipping company has made some changes, and the new capacities and prices are shown in the following. Suppose that you have 4 different products to ship and 2 box sizes—small and large. Review the following data:

Product	Weight	Per small box	Per large box
I	6.19	16	24
II	2.98	28	47
III	5.23	17	28
IV	4.52	21	31

Price per box
Prod	Small	Large
I	5.98	8.27
II	4.73	7.61
III	6.60	7.25
IV	6.02	9.19

 Suppose that you want to ship 800, 700, 775, and 925 units of products I–IV, respectively, and you must arrange them into boxes to minimize total cost. Note that a partially filled box will ship for the same price as a full box.

The shipper has re-instituted the rule that small boxes ship in groups of 7. A partial group costs the same as a whole group.

Suppose that you make a mistake in formulating the problem and charge the per-box cost for each bundle of small boxes. What is the predicted cost to ship all the products? Round to the nearest dollar.

$155

$644

$630

$623

Helen’s transportation company tries to deliver the following crops. There are a total of 600 boxes of apples, 500 boxes of bananas, 450 boxes of nectarines, and 350 boxes of peaches. These equal sized boxes can carry up to 25 pounds of apples, 35 pounds of bananas, 45 pounds of nectarines, and 30 pounds of peaches. The shipping charge for apples, bananas, nectarines, and peaches are $6.35, $6.45, $6.35, and $6.50 per box, respectively. The truck has a weight limit of 40,000 pounds and a capacity not more than 1,200 boxes.

Question 5

What is the weight limit constraint?

25A + 35B + 45N + 30P ≤ 40,000

25 + 35 + 45 + 30 ≤ 40,000

A + B + N + P ≤ 40,000

25A + 35B + 45N + 30P ≥ 40,000

Question 6

Your shipping company has made some changes, and the new capacities and prices are shown in the following. Suppose that you have 4 different products to ship and 2 box sizes—small and large. Review the following data:

Product	Weight	Per small box	Per large box
I	6.19	16	24
II	2.98	28	47
III	5.23	17	28
IV	4.52	21	31

 

Price per box
Prod	Small	Large
I	5.98	8.27
II	4.73	7.61
III	6.60	7.25
IV	6.02	9.19

 Suppose that you want to ship 800, 700, 775, and 925 units of Products I–IV, respectively, and you must arrange them into boxes to minimize total cost. Note that a partially filled box will ship for the same price as a full box.

What is your total shipping cost? Round to the nearest dollar.

$1,012

$937

$868

$643

Helen’s transportation company tries to deliver the following crops. There are a total of 600 boxes of apples, 500 boxes of bananas, 450 boxes of nectarines, and 350 boxes of peaches. These equal sized boxes can carry up to 25 pounds of apples, 35 pounds of bananas, 45 pounds of nectarines, and 30 pounds of peaches. The shipping charge for apples, bananas, nectarines, and peaches are $6.35, $6.45, $6.35, and $6.50 per box, respectively. The truck has a weight limit of 40,000 pounds and a capacity not more than 1,200 boxes.

Question 7

Which of the following crops did she completely deliver after running the problem through Excel’s Solver?

Nectarines and peaches

Apples and bananas

Apples

Bananas and peaches

Question 8

What resource does Helen run out first in delivering the crops?

Weight

Neither capacity nor weight

Both capacity and weight

Capacity

Question 9

What should the shipping charge per box of nectarines be changed to in order for her to deliver all of the nectarines after running the problem through Excel’s Solver?

$6.95

$6.96

$6.35

$6.00

Question 10

Your shipping company has made some changes, and the new capacities and prices are shown in the following. Suppose that you have 4 different products to ship and 2 box sizes—small and large. Review the following data:

Product	Weight	Per small box	Per large box
I	6.19	16	24
II	2.98	28	47
III	5.23	17	28
IV	4.52	21	31

 

Price per box
Prod	Small	Large
I	5.98	8.27
II	4.73	7.61
III	6.60	7.25
IV	6.02	9.19

 Suppose that you want to ship 800, 700, 775, and 925 units of products I – IV respectively, and you must arrange them into boxes to minimize total cost. Note that a partially filled box will ship for the same price as a full box.

The shipper has re-instituted the rule that small boxes ship in groups of 7. A partial group costs the same as a whole group. It turns out only one of the products ships in small boxes.

How many bundles of 7 small boxes of product can you ship? Which product is it?

20; II

6; IV

11; III

11; IV

Question 11

Your shipping company has made some changes, and the new capacities and prices are shown in the following. Suppose that you have 4 different products to ship and 2 box sizes—small and large. Review the following data:

Product	Weight	Per small box	Per large box
I	6.19	16	24
II	2.98	28	47
III	5.23	17	28
IV	4.52	21	31

 

Price per box
Prod	Small	Large
I	5.98	8.27
II	4.73	7.61
III	6.60	7.25
IV	6.02	9.19

 Suppose that you want to ship 800, 700, 775, and 925 units of Products I–IV, respectively, and you must arrange them into boxes to minimize total. Note that a partially filled box will ship for the same price as a full box.

The shipper has re-instituted the rule that small boxes ship in groups of 7. A partial group costs the same as a whole group.

What is the cost to ship all of the products? Round to the nearest dollar.

$870

$963

$880

$1,091

Helen’s transportation company tries to deliver the following crops. There are a total of 600 boxes of apples, 500 boxes of bananas, 450 boxes of nectarines, and 350 boxes of peaches. These equal sized boxes can carry up to 25 pounds of apples, 35 pounds of bananas, 45 pounds of nectarines, and 30 pounds of peaches. The shipping charge for apples, bananas, nectarines, and peaches are $6.35, $6.45, $6.35, and $6.50 per box, respectively. The truck has a weight limit of 40,000 pounds and a capacity not more than 1,200 boxes.

Question 12

What is the objective function?

Maximize load value = $6.35 + $6.45 + $6.35 + $6.50

Minimize load value = $6.35A + $6.45B + $6.35N + $6.50P

Maximize load value = $6.35A + $6.45B + $6.35N + $6.50P

Maximize load value = A + B + N + P