Agame is played as follows: a die numbered 1 to 6 is rolled. if the number 1 comes up, you get nothing. if the number 2, 3, or 5 comes up, you win $4. if the number 4 or 6 comes up, you lose $6. according to the expected value, this is a fair game. true or false

Your vet has placed your pet on a diet. the diet is to contain at least 12 mg of fat and at least 14 mg of protein per serving. these requirements are to be obtained from two food sources. source a contains 2 mg of fat and 2 mg of protein per serving. source b contains 1 mg of fat and 3 mg of protein per serving. if source a sells for $1.28 per serving and source b sells for $1.12 per serving, how many servings of each type should be purchased to satisfy the requirements at minimal cost?