Hi irish_traveller!!
Well, this is a tricky question and the answer results very short and
may be a surprising one.
The answer is D as you was told, that is if Ben makes 254 boxes of
cookies in the cheapest way possible, he will use zero canisters of
soybean oil.
Why? you ask. It is easy, first note that sugar and oils are not the
only ingredients of the cookies, there are others; but the amount of
production depends only on 3 variables the number of bags of sugar,
the number of canisters of peanut oil, and so the number of canisters
of soybean oil used.
Well, when Ben wants to produce cookies in the cheapest way possible
he only use the cheapest ingredients.
It is easy to see that peanut oil and soybean oil are substitutes,
that is you can use one instead the other or both together; but prices
are different, each canister of soybean oil cost $19 and the price of
a canister of peanut oil is $6.
Ben want to make cookies in the cheapest way possible so he will use
only the needed amount of cheapest oil, in this case peanut oil, and
no soybean due its high cost. This is why the answer is zero canister
of soybean will be used.
Regarding the meaning of "f(su,po,so) = min {su, po + 2so}":
The statement of the problem says that the number of boxes of cookies
produced is function of the following variables or factors:
su: number of bags of sugar used,
po: number of canisters of peanut oil used, and
so: number of canisters of soybean oil used.
The production function is called f and the notation "f(su,po,so)"
indicates which are the independent variables of the function.
The notation "f(su,po,so) = min {su, po + 2so}" (better written as
"min{su,(po+2*so)}", where the asterisk denotes the common product,
like in 2*3=6) describes the function f indicating which values the
production reach according to the values of the independent variables.
"min" means minimum, then f(su,po,so) = min{su,(po+2*so)} means that:
The number of number of boxes of cookies that produced is equal to THE
MINIMUM VALUE BETWEEN THE FOLLOWING 2 NUMBERS:
a) su
b) po+2*so
For example if he uses 10 bags of sugar, 5 canisters of peanuts oil
and 3 canisters of soybean oil, we have that:
a) su = 10
b) po+2*so = 5 + 2*3 = 11 ;
then:
f(su,po,so) = min{su,(po+2*so)} =
= min{10,11} =
= 10
Therefore Ben will produce 10 boxes of cookies.
I hope this helps you to understand the problem and its solution. feel
free to request for a clarification if you need it.
Regards,
livioflores-ga |