Math451 Unit2 Allocations Interactive Example
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Feb 20, 2024
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Math451
Unit 2 Allocation
Interactive Examples
Helen’s transportation company tries to deliver the following crops with two identical trucks. 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. Each truck has a weight limit of 32,000 pounds and a capacity not more than 1,000 boxes.
Question 1
Which of the following crops did she completely deliver after running the problem through Excel’s Solver?
Apples, bananas, and peaches
Bananas, nectarines, and peaches
Apples, bananas, and nectarines
All of the crops
Solution
The correct answer is:
All of the crops
Correct
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Question 2
Which crop is not loaded onto Truck #1 if shipping costs are maximized?
Apples and nectarines
Nectarines
Peaches
Apples
Solution
The correct answer is:
Nectarines
Correct
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Question 3
Consider a trucking company that is delivering the following crops:
500 boxes of apples, 25 pounds each
450 boxes of bananas, 35 pounds each
400 boxes of nectarines, 45 pounds each
400 boxes of peaches, 30 pounds each
The shipping charge for apples, bananas, nectarines, and peaches are $6.10,
$6.35, $6.20, and $6.40 per box, respectively. The truck has a weight limit of
35,000 pounds and a capacity of no more than 1,100 boxes. The goal is to maximize the total shipping charge.
The trucking problem above features several different limits.
Modify the problem slightly using the following information:
Product
Weight
Value
Number
Apple
25
6.1
600
Banana
35
6.35
500
Nectarine
45
6.2
550
Peach
30
6.55
650
Suppose that instead of one big truck, you have three smaller ones, each with a weight limit of 20,000 and a package limit of 900. Suppose that you could increase either the weight limit by 4,000 or the package limit by 120.
What would be the increase in the value of the shipments? Round your answer to the nearest dollar.
If you increase the package limit by 120, the total value will be up by $735.
If you increase the package limit by 120, the total value will be up by $1,662.
If you increase the weight limit by 4,000, the total value will be up by $2,317.
If you increase the weight limit by 4,000, the total value will be up by $1,662.
Solution
The correct answer is
If you increase the weight limit by 4,000, the total value will be up by $1,662.
Correct
Hide solution
Helen’s transportation company tries to deliver the following crops with two identical trucks. 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. Each truck has a weight limit of 32,000 pounds and a capacity not more than 1,000 boxes.
Question 4
What is the value for the objective function after running the problem through Excel’s Solver?
$32,000
$12,167.50
$7,722.50
$1,000
Solution
The correct answer is:
$12,167.50
Correct
Hide solution
Question 5
Consider a trucking company that is delivering the following crops:
500 boxes of apples, 25 pounds each
450 boxes of bananas, 35 pounds each
400 boxes of nectarines, 45 pounds each
400 boxes of peaches, 30 pounds each
The shipping charge for apples, bananas, nectarines, and peaches are $6.10,
$6.35, $6.20, and $6.40 per box, respectively. The truck has a weight limit of
35,000 pounds and a capacity of no more than 1,100 boxes. The goal is to maximize the total shipping charge.
If you abstract from this, you get products
, weight per product
, and price or value per product,
.
What is missing?
The limit on the total number of products that can be shipped
The cost of the truck
The objective function
, where
is the number of each product shipped
The total weight shipped
, where
is the number of each product shipped
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Solution
The correct answer is
The limit on the total number of products that can be shipped
Correct
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