# Math Help - Linear Programming Word Problem; system of inequalities

1. ## Linear Programming Word Problem; system of inequalities

A hospital dietician wishes. To prepare a corn-squash vegetable dish that will provide at least 3 grams of protein and cost no more that .36 per serving. And ounce of cream corn provides 1/2 gram of protein and costs .04. An ounce of squash supplies 1/4 gram of protein and costs .03. For taste, there must be at least 2 ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corrn and squash that will minimize the amount of ingrediants used per serving. I am horrible at word problems and I've been trying to get the hang of it, please help.

2. ## Re: Linear Programming Word Problem; system of inequalities

Let "C" be the number of oz of creamed corn and "S" be the number of oz of squash, per serving.

"ounce of cream corn provides 1/2 gram of protein" and "An ounce of squash supplies 1/4 gram of protein" so C oz of corn and S oz of squash provide C/2+ S/4 grams of protein.
"provide at least 3 grams of protein" so you must have $C/2+ S/4\ge 3$

And ounce of cream corn costs .04" and "An ounce of squash costs .03" so C oz of corn and S oz of squash cost .04C+ .03S.
"cost no more that .36 per serving" so you must have $.04C+ .03S\le .36$.

"For taste, there must be at least 2 ounces of corn and at least as much squash as corn." so $C\ge 2$ and $S\ge C$.

"minimize the amount of ingrediants used per serving"
Minimize C+ S.

3. ## Re: Linear Programming Word Problem; system of inequalities

Thank you! That's what I thought. What equation do I use to find the min and max values?

4. ## Re: Linear Programming Word Problem; system of inequalities

Oh, nevermind! I got it (: