You work as a chemical engineer, your job is to combine various chemicals to pro
ID: 334439 • Letter: Y
Question
You work as a chemical engineer, your job is to combine various chemicals to produce pharmaceutical medicine. One day, your boss cannot make it to work, so you are in charge. You get a panicked phone-call from a hospital; the hospital urgently needs their delivery of Medicine X. Unfortunately, you don't have any of this particular medicine ready, and it's one that you have not made before (normally your boss handles Medicine X). Because of this, you are not sure how it is made (you are not sure how much of which chemicals mix together to produce Medicine X) You look through the documents your boss has that are relevant to this client. Although you don't find a recipe for Medicine X, you do find the electronic accounting ledger where your boss has calculated the cost of producing Medicine X the last three times it was produced (most recent entry in row 1) Cost of r Cost of y Cost of Total cost to uce MedicineX 19,000 21,000 20.000 2 It is noted in the ledger that each chemical's cost is given in dollars per unit of chemical. You also remember your boss ranting about how chemical prices kept changing, making it hard for him to keep profit predictable. You also note that the hospital ordered the same quantity of Medicine X each time, which is the same quantity that they want now From the ledger, you can see that Medicine X is produced using chemical r, chemical y and chemical z. (a) By forming an appropriate matrix system and applying Gaussian Elimination to an augmented matrix, show that the required quantities of chemical z, chemical y and chemical z are 2500, 1000 and 3000 respectively b) Once the boss returns, they make more than one batch of Medicine X at a time. Your facility allows you to produce batches 5 or 10 times larger than your current batch size. They note that if you made larger batches the company could negotiate better prices from their chemical suppliers. They estimate the following discounts on the most recent ledger prices (first row of ledger) you on your great work. Your boss never had the time to . 25% off the price of each chemical (x, y and z) if purchasing five times the original amount of each. . 30% off the price of each chemical (x, y and z) if purchasing ten tines the original amount of each. If you make larger batches, you will need to add a preservative to the product to increase the shelf life. The preservative costs $10,000 per unit. Based on how frequently Medicine X is ordered, the boss determines that the preservative must be added as follows: 2 units of preservative if producing five times the original amount of Medicine X, 5 units of preservative if producing ten times the original amount of Medicine X. i) Complete the following table describing the costs associated with producing different amounts of Medicine X Batch size Total cost Total cost of preservatives Total cost of production 10 ii) Based on this information, determine the most cost effective batch sizeExplanation / Answer
Current average price of products
x=(2+2+2)/3=2=Cx
y=(2+1+3)/3=2=Cy
z=(4+5+4)/3=4.33=Cz
Cost of production=Cost per quantity * total quantity required by recipe
Quantity X=2500=Qx
Quantity Y=1000=Qy
Quantity z=3000=Qz
=Qx*Cx+Qy*Cy+Qz*cz
=2500*2+1000*2+3000*4.33
=20000
=Qx*Cx+Qy*Cy+Qz*cz
Discount of 25%
100%-25%=75%=0.75 of previous cost
=(2500*2+1000*2+3000*4.33)*(0.75)
=15000
Total units produced =5
TotaL cost=75000
Units required=2
Cost per unit =10000
Total cost=20000
Total cost = 75000+20000
=95000
Cost per units=95000/5
=19000
=Qx*Cx+Qy*Cy+Qz*cz
Discount of 30%
100%-30%=70%=0.7 of previous cost
=(2500*2+1000*2+3000*4.33)*(0.7)
=14000
Total units produced =10
TotaL cost=140000
Units required=5
Cost per unit =10000
Total cost=50000
otal cost = 140000+50000
=190000
Cost per units=190000/10
=19000
B. Batch of 5 & 10 are equally effective
Batch Size Total Cost of chemicals Total cost of pres. Total cost of produc. 1=Qx*Cx+Qy*Cy+Qz*cz
=2500*2+1000*2+3000*4.33
=20000
0 20000 5=Qx*Cx+Qy*Cy+Qz*cz
Discount of 25%
100%-25%=75%=0.75 of previous cost
=(2500*2+1000*2+3000*4.33)*(0.75)
=15000
Total units produced =5
TotaL cost=75000
Units required=2
Cost per unit =10000
Total cost=20000
Total cost = 75000+20000
=95000
Cost per units=95000/5
=19000
10=Qx*Cx+Qy*Cy+Qz*cz
Discount of 30%
100%-30%=70%=0.7 of previous cost
=(2500*2+1000*2+3000*4.33)*(0.7)
=14000
Total units produced =10
TotaL cost=140000
Units required=5
Cost per unit =10000
Total cost=50000
otal cost = 140000+50000
=190000
Cost per units=190000/10
=19000
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