Operations research word problem help appreciated

[lauraanderson]

I was wondering if anyone would be able to help me in answering these two questions related to this problem. I'm rather stuck!

Problem - Ronald has just discovered four new ingredients for making a very potent potion that will raise his IQ by 15 points. We can only identify the ingredients as A, B, C and D, which combines several traditional ingredients. The decision variables are therefore xA; xB; xC and xD, which represents the amounts of each ingredient we use. To protect his secrets, Ronald has chosen to keep one of his constraints secret.

What is the current cost of using these ingredients?

The supplier of xA has reduced its price to 1 dollar. How would this affect the quantities of the ingredients used and what is the new optimal cost of the potion?

 

[Ray Vickson]

I was wondering if anyone would be able to help me in answering these two questions related to this problem. I'm rather stuck!

Problem - Ronald has just discovered four new ingredients for making a very potent potion that will raise his IQ by 15 points. We can only identify the ingredients as A, B, C and D, which combines several traditional ingredients. The decision variables are therefore xA; xB; xC and xD, which represents the amounts of each ingredient we use. To protect his secrets, Ronald has chosen to keep one of his constraints secret.

What is the current cost of using these ingredients?

The supplier of xA has reduced its price to 1 dollar. How would this affect the quantities of the ingredients used and what is the new optimal cost of the potion?

What have you done so far on this problem? Show your work. In particular: you know the ingredient unit costs and you know the amounts used, so what is stopping you from computing the total cost?