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Q: Cost Minimization Microeconomics Managerial Economics ( Answered ,   0 Comments )
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 Subject: Cost Minimization Microeconomics Managerial Economics Category: Business and Money Asked by: irish_traveller-ga List Price: \$20.00 Posted: 27 May 2006 14:38 PDT Expires: 26 Jun 2006 14:38 PDT Question ID: 732909
 ```Hi below is the question I am having so much troube with. I have been told the answer is D but I have no idea how to get it. If anyone knows how to it will be much appreciated also please explain all working! Especially what the notation min {su, po + 2so} means (I think its an easy question I just dont know what that notation means!!!) Ben runs a cookie factory. His cookies are made with sugar, peanut oil, and soybean oil. The number of boxes of cookies that he produces is f (su, po, so) = min {su, po + 2so}, where su is the number of bags of sugar, po the number of canisters of peanut oil, and so the number of canisters of soybean oil that he uses. The price of a bag of sugar is \$12. The price of a canister of peanut oil is \$6. The price of a canister of soybean oil is \$19. If Ben makes 254 boxes of cookies in the cheapest way possible, how many canisters of soybean oil will he use? A. 84.67 B. 127 C. 169.33 D. 0 E. 42.33```
 ```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``` Request for Answer Clarification by irish_traveller-ga on 28 May 2006 06:57 PDT ```Thank you so much for your answer, you've really helped me out! :D One thing I need clarifcation for is "it is easy to see peanut oil and soybean oil are perfect substitutes", how would a student know this from the question?``` Request for Answer Clarification by irish_traveller-ga on 28 May 2006 07:22 PDT ```I have posted another question on this topic and would really appreciate your help on that too``` Clarification of Answer by livioflores-ga on 28 May 2006 08:13 PDT ```Hi again!! You asked: "One thing I need clarifcation for is "it is easy to see peanut oil and soybean oil are perfect substitutes", how would a student know this from the question?" There is no way to know that from the statement, this is why it is a tricky question. May be I did not use the more appropriate expression at this point, but both are oils and not an essential part of the recipe (if you know a little about cooking). Hope this helps. Regards, livioflores-ga``` Request for Answer Clarification by irish_traveller-ga on 28 May 2006 08:39 PDT `Thanks livioflores, if ur on now could you take a look at my other question?` Clarification of Answer by livioflores-ga on 28 May 2006 19:10 PDT `Thank you for the good rating!!`
 irish_traveller-ga rated this answer: `Very helpful, good long answer`