Food for Thought WS - Linear Programming

[Yuimei]

I'm having a difficult time figuring out linear programming when there are three things to solve:
Nutritionists indicate that an adequate daily diet should provide at least 75g of carbohydrate, 60 g of protein, and 60g of fat. An ounce of food A contains 6g of carbohydrate, 2 g or protein, and 3g of fat. An ounce of food B contains 3g of carbohydrate, 4g of protein, and 3g of fat. Also, the number of calories per day should not be more that 1500. An ounce of food A contains 75 calories, and an ounce of food B contains 50 calories. Food A costs 10¢ an ounce, and food B costs 15¢ an ounce. How many ounces of each food should be combined per day to meet the nutritional requirements at the minimum cost?

I couldn't really figure anything out, like the first step to set this up. All I have so far is:
75x ? 1500
50x ? 1500

Profit: 10x + 15y

Please help

 

[mmm4444bot]

Hello:

You did not define your symbols x and y, so your beginning work is meaningless.

After reading a word problem sufficiently, to understand the given scenario and that which is requested, the next step is almost always to pick symbols to represent the unknowns, followed by writing down the definitions for your symbols.

Like this:

a = the number of ounces of food A

b = the number of ounces of food B

Did you organize the given information? Filling-out a quick chart might be useful, for this.

That makes it easier to "see" the following.

Ingesting a ounces of food A and b ounces of food B provides:

6a + 3b grams of carbohydrates

2a + 4b grams of protein

3a + 3b grams of fat

75a + 50b calories

Use these expressions to write your inequalities.

The objective expression represents the cost of a ounces of food A plus b ounces of food B:

cost = 0.10a + 0.15b

This is the expression that you want to minimize. After you determine the (a,b) coordinates of the system-of-inequalities-solution-area vertex points, use those ordered pairs to evaluate the objective expression, in order to discover which (a,b) pair leads to the smallest cost.

Profit is not involved, in this exercise. Profit is money left over after you subtract your costs from your revenue. You must be thinking of another exercise.

Please show your work, if you would like more help with this exercise.

Cheers ~ Mark