SOLUTION: You are attending Thanksgiving at your family member's house and agreed to bring two side dishes with you; potatoes and corn. You are on a budget though and can only spend $30 in t

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Question 1179843: You are attending Thanksgiving at your family member's house and agreed to bring two side dishes with you; potatoes and corn. You are on a budget though and can only spend $30 in total. You determined that you need at least 10 pounds of food to have enough for all your relatives. Potatoes cost $0.75 per pound and corn costs $1 per pound. The preparation time to peel each pound of potatoes is 15 minutes and to shuck each pound of corn takes 9 minutes. You absolutely hate preparing food and want to minimize the amount of time you need for it. Use the variable "p" to represent number of pounds of potatoes and "c" to represent number of pounds of corn.
a) State what your objective function is, in words, and then write out an equation that represents it.
b) Write out your constraints for the cost and quantity as inequalities. There should be 4 constraints in total.
I'm sorry if I asked that question for the category "Linear equations" and it should be in "Inequalities". Anyway, can you please help me with this homework problem by explaining it step-by-step? Once again, I apologize for my error.
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.

Write inequality for total food

    p + c >= 10 pounds    (1)    (total food)



Write inequality for money to be in budget

    0.75*p + 1*c <= 30    dollars.



The amount of time is 

    15p + 9c  minutes,


and you want to minimize it.


There are also inequalities of non-negativity

    p >= 0,  c >= 0.


So, I wrote the inequalities you were asked for.


    +--------------------------------------------+
    |   The solution to the problem is OBVIOUS.  |
    +--------------------------------------------+


If you want minimize your time, prepare 10 pounds of corn
and do not touch potatoes.



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