An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 25 units of fiber, 40 units of protein, and 40 units of fat. Each case of Brand B contains 100 units of fiber, 130 units of protein, and 110 units of fat. Each case of Brand C contains 275 units of fiber, 350 units of protein, and 310 units of fat. Each case of Brand D contains 200 units of fiber, 260 units of protein, and 200 units of fat. How many cases of each brand should the breeder mix together to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat? Let \( x \) represent the number of cases of Brand A, y represent the number of cases of Brand B, z represent the number of cases of Brand C, and w represent be the number of cases of Brand \( D \). There are four ways in which the breeder can mix brands to obtain a food that provides 3975 units of fiber, 5100 units of protein, and 4440 units of fat. If \( w=0 \), the solution is \( (0,15,9,0) \). If \( w=1 \), the solution is \( (\square, \square, \square, 1) \).
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Let’s dive into the world of feeding your Vietnamese pot-bellied pigs! When mixing these brands, you’ll want to keep some variables under control while juggling fiber, protein, and fat content. It’s like being a chef, but for a piggy feast! Now, about those cases: if you take \( w=1 \) (meaning you’re using one case of Brand D), you can plug that into your equations and solve for \( x \), \( y \), and \( z \). Using those total nutrition units, calculate the rest. It’s a bit of a balancing act, but with a few equations and some creativity, you can whip up the perfect piggy meal plan! Remember not to get too carried away; overly rich food might contribute to an overly plump pig!
