QuestionQuestion

Transcribed TextTranscribed Text

Assignment 2: A manufacturing firm produces and sells a product to a single independent retailer. The product is sold during a single selling season. The manufacturer has production cost is $6.00 per unit and the retailer sells the product to the consumers at a price of $28.00 per unit. Unsold units at the end of the selling season have a salvage value of $2.00. If the retailer cannot meet the demand during the selling season then she has a goodwill penalty cost of $3.00 and the manufacturer has a goodwill penalty cost of $2.5. To procure the product the retailer has a cost of $1.00 per unit. The retailer places an order with the manufacturer at the start of the selling season and the delivery is instantancous The consumer demand x follows a Gamma distribution in the interval (0,co) with shape parameter a - 1 and scale parameter ß - 100. Hint: The Gamma distribution has the probability density function 1 f(x) T(a) 8° Where l(a) is called the Gamma function defined as r(n) - (n - 1)!. The expected value of the Gamma distribution is EX aß In Excel the Gamma distribution can be found by the formula GAMMADIST (English) and the inverse of the Gamma distribution can be found by the formula GAMMA.INV (English). For students who used Excel in Danish or other languages, please use the Excel help or google to find the corresponding formulas in Excel. You have to solve the exercises A-F below and they are weighted evenly. A) With the parameters given above you have to 1 1. Show that the probability density function has the formf(x) = 100 100 2. Show that the distribution function has the form F(x)-1-e- - 3. Show that the expected sale has the form S(q) - 100(1-e - 4. Construct a diagram showing the expected dernand, the expected sales, the expected leftover inventory and expected lost sales as functions of the retailer's order quantity. B) Suppose that the supply chain members make joint decisions 1. Which order quantity is the optimal for the supply chain? 2. What is the optimal supply chain profit?

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf and calc.m.

    $35.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Business - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats