Xtreme Sands Inc

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School

Arizona State University *

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Course

2551

Subject

Material Science

Date

Apr 3, 2024

Type

pdf

Pages

2

Uploaded by GrandRain13709

Pleace list vour team members here Xtreme Sands, Inc,, blends different colored sands together to create unique mixtures, and sell these mixtures to Art & 8 { Craft stores for kids. These sand mixtures, when combined & / 4 with flour and water, will have a doughy texture, which can N be sculpted to form different shapes. The company sells 3 different signature mixes: Cherry, Mango, and Blueberry. Each mixture is obtained by blending red, yellow, and blue sands together in different proportions. The recipe for creating these mixtures is as follows. e Cherry: Requires at least 50% red sand, at least 10% yellow sand. However, the Cherry mixture cannot have more than 20% blue sand (possibly zero). e Mango: Requires at least 60% yellow sand, and equal parts of red and blue sand (possibly zero). e Blueberry: Requires atleast 70% blue sand, at least 5% of red sand. However, the Blueberry mixture cannot have more than 10% yellow sand (possibly zero). The market price (per gram) for each mixture is given in the following table: Mixture Cherry Mango Blueberry Price (in dollars) per gram $1.10 $1.20 $1.00 The current supplies of colored sand are given below Sand Color Red Yellow Blue Supply (in grams) 28 20 25 Make sure that your scale is set to measure the sand in grams. You should see the letter “g” appearing on the top right corner of your scale. Also, the plastic bag containing each type of sand weights around 0.9 - 1.1 g Please answer the following TWO questions on the next page. Page 1 of 2
produce in order to d the company Fhere are two Wow misch of each mixture shoul mal total revenue? NOTE Question #1 and what is the opti mavimize the total revenue parts to this question 2t of Sz oin | [ | Amount of Sand Use in ‘ Cherty | Mango | Blueberry Each Mixture | | [ 5 Red Sand J Yellow Sand Blue Sand Total Mixture Produced (in grams) The optimal total revenue is eceive credit for Question #1, you must also physically fill the IMPORTANT: Tor! ree bottles given in your sand kit. appropriate amount of sand into the appropriate th e supplier of blue sand is experiencing a severe manufacturing rtainty about the amount of available blue sand. The de between 0 and 12 grams of blue sand, and every available blue sand is Question #2:_ Suppose th problem, causing a significant unce supplier indicates that it can only provi value in between 0 and 12 is equally likely. So, the amount of uniformly distributed between 0 and 12 grams. Assume that all other parameters remain constant. Taking into account the uncertainty in the supply of blue sand, what is the optimal expected total revenue that Xtreme Sands can make? Please report your answer with at least 2 decimal points. HINT: Changing the blue sand quantity to 6 = (0+12)/2 grams and re-run the Solver, which will give you a value of $62.32, is NOT correct. A simple averaging of the optimal revenue under 12 grams of blue sand and the optimal revenue under 0 gram of blue sand, yielding the value of $61.64, is also NOT correct. Finally, using simulation will NOT give you the correct answer. Page 2 of 2
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