TJ, Inc. makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts. In preparation for the fall season, TJ, Inc. just purchased the following shipments of nuts at the prices shown: Type of Nut Shipment Amount (pounds) Cost per Shipment ($) Almond 6,100 7,500 Brazil 7,400 7,025 Filbert 7,400 6,750 Pecan 6,000 7,100 Walnut 7,400 7,875 The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts. The Deluxe Mix consists of 20% of each type of nut, and the Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts.   An accountant at TJ, Inc. analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $1.70 for the Regular Mix, $2.05 for the Deluxe Mix, and $2.20 for the Holiday Mix. These figures do not include the cost of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets.   Customer orders already received are summarized here: Type of Mix Orders (pounds) Regular 10,000 Deluxe 3,000 Holiday 5,000 Because demand is running high, it is expected that TJ, Inc. will receive many more orders than can be satisfied. TJ, Inc. is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to a local charity. Even if it is not profitable to do so, TJ, Inc.'s president indicated that the orders already received must be satisfied. Managerial Report Perform an analysis of the TJ, Inc.'s product-mix problem, and prepare a report for the president of TJ, Inc. that summarizes your findings. Cost Per Pound of the Nuts Included a. Determine the cost per pound of the nuts included in the Regular mix (in dollars). (Round your answer to two decimal places.) $  per pound b. Determine the cost per pound of the nuts included in the Deluxe mix (in dollars). (Round your answer to two decimal places.) $  per pound c. Determine the cost per pound of the nuts included in the Holiday mix (in dollars). (Round your answer to two decimal places.) $  per pound   d. Determine the optimal product mix (in pounds). Regular lbDeluxe lbHoliday lb e. Determine the total profit contribution (in dollars). $

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Topic Video
Question
TJ, Inc. makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts.
In preparation for the fall season, TJ, Inc. just purchased the following shipments of nuts at the prices shown:
Type of Nut Shipment Amount (pounds) Cost per Shipment ($)
Almond 6,100 7,500
Brazil 7,400 7,025
Filbert 7,400 6,750
Pecan 6,000 7,100
Walnut 7,400 7,875
The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts. The Deluxe Mix consists of 20% of each type of nut, and the Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts.
 
An accountant at TJ, Inc. analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $1.70 for the Regular Mix, $2.05 for the Deluxe Mix, and $2.20 for the Holiday Mix. These figures do not include the cost of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets.
 
Customer orders already received are summarized here:
Type of Mix Orders (pounds)
Regular 10,000
Deluxe 3,000
Holiday 5,000
Because demand is running high, it is expected that TJ, Inc. will receive many more orders than can be satisfied.
TJ, Inc. is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to a local charity. Even if it is not profitable to do so, TJ, Inc.'s president indicated that the orders already received must be satisfied.
Managerial Report
Perform an analysis of the TJ, Inc.'s product-mix problem, and prepare a report for the president of TJ, Inc. that summarizes your findings.
  • Cost Per Pound of the Nuts Included

    a. Determine the cost per pound of the nuts included in the Regular mix (in dollars). (Round your answer to two decimal places.)
    $  per pound
    b. Determine the cost per pound of the nuts included in the Deluxe mix (in dollars). (Round your answer to two decimal places.)
    $  per pound
    c. Determine the cost per pound of the nuts included in the Holiday mix (in dollars). (Round your answer to two decimal places.)
    $  per pound
     
    d. Determine the optimal product mix (in pounds).
    Regular lbDeluxe lbHoliday lb
    e. Determine the total profit contribution (in dollars).
      
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 23 images

Blurred answer
Knowledge Booster
Inventory management
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,