vet designs special diet for cat.... Find least-cost mix

[odysseus]

Would someone please outline the steps for this question, but without actually answering it?

A vet designs a special diet for a cat. This diet requires that the cat be allowed no more than 1500 calories, but at least 400 g protein. The vet can special-order the animal's food, but would prefer instead to mix to ready-made foods. (The question gives me two foods, with the calories, protein, and cost per tin listed.) List the constraints, and find a mixture which provides an adequate diet at the lowest costs.

I would like to understand the steps, which is why I have been vague with the details. Thanks in advance for your advice.

[stapel_eliz]

I would like to understand the steps...

For a general outline of the steps, try this lesson on linear programming.

For this particular exercise, since you are asked for the amounts of the two foods, your variables should stand for the amounts of those foods. It sounds like you are working with entire tins (American English: cans) of food, which makes sense: once you've opened the can, you'd better use it, because the extra will just have to be discarded anyway.

If you label the foods as Food X and Food Y, with the numbers of tins used being "x" and "y", respectively, then you have:

. . . . .(number of ounces in a tin of Food X)*x + (no. of oz. in a tin of Food Y)*y < 1500

. . . . .(grams protein in a tin of Food X)*x + (gm pro. in a tin of Food Y)*y > 400

. . . . .(calories in a tin of Food X)*x + (cal. in a tin of Food Y)*y (some inequality) (some calorie count)

You'll also have the usual constraints, being x > 0 and y > 0. Then you'll minimize P = (cost of a tin of Food X)*x + (cost of a tin of Food Y)*y.

Hope that makes sense!

[odysseus]

Yes, that made plenty of sense. Thank you for your time.