Min utility function doubt.

[MR]

Rocco's Pasta Bar makes manacotti according to an old family recipe which states M= min{3/2C,3P}, where
M, C,and P are pounds of manicotti, cheese, and pasta respectively. If cheese costs $3 per pound and pasta costs $1 per pound, how much would it cost to produce 10 pounds of manicotti in the cheapest way possible?
The answer is $20. If anyone arrives to the answer please post your method here. Will be very grateful. :)

[Devika]

I'm getting 23.33

[MR]

Ok. But how did you get that? Can you show the workings. I guess 23.33 was there in the options. Maybe I saw the wrong answer. Still share your method. I could go till the point where C=2P.

[Devika]

The cost function came out to be-

C = q(Pc/1.5 + Pp/3)

Substitute the relevant values, q=10, Pc=3, Pp=1

[MR]

Thanks. :)