Question

A plastic material supplier has developed a proprietary additive package to improve molding characteristics of their product. The additive consists of two proprietary compounds, K and T. K for example contains 10 grams/lb of calcium, with the mix requiring at least 40 grams/batch. The active ingredients in K and T are listed below, with the minimum required amounts of each. Identify the mix of K and T that meets all required amounts and minimizes cost.

Grams/lb. of each	K	T	Required per batch
Dihydrogen monoxide	15.00	6.00	30.00
Calcium	10.00	10.00	40.00
Alumina	3.00	9.00	18.00
Cost per pound	$ 1.50	$ 0.70

Question 15 options:

1)

K=3, T=1

2)

K=1, T=3

3)	K=0.67, T=2.67

4)

K=0, T=4

Answer 1

Answer:

• Option 2: K=1 and T=3

Explanation:

• Simply evaluating amount of each ingredient for each option:
  • Option 1. Dihydrogen = 45+6 = 51 , Calcium = 30+10 =40 , Alumina= 9+9 =18
  • Option 2. Dihydrogen = 15+18 = 33 , Calcium = 10+30 =40 , Alumina= 3+27 =30
  • Option 3. Dihydrogen = 10+16 = 26 , Calcium = 6.67+26.7 =33.33 , Alumina= 2+24 =26
  • Option 1. Dihydrogen = 24 , Calcium = 40 , Alumina=36
• So only option 1 and 2 satisfy the requirement per batch
• Out which option 2 has lower cost ($3.6) , hence option 2