A merchant makes two raisin nut mixtures.
Each box of mixture A contains 9 ounces of peanuts and 2 ounces of raisins, and sells for $2.80. Each box of mixture B contains 12 ounces of peanuts and 4 ounces of raisins, and sells for $4.00. The company has available 5,000 ounces of peanuts and 1,800 ounces of raisins. The merchant will try to sell the amount of each mixture that maximizes income.
Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B.
1) State the objective function.
A. 5,000x + 1,800y
B. 9x + 2y
C. 9x + 12y
D. 2.8x + 4y
2. Since the merchant has 1,800 ounces of raisins available, one inequality that must be satisfied is:
A. 2x + 4y ¡Ü 1,800
B. 2.8x + 4y ¡Ü 1,800
C. 4x + 2y ¡Ý 1,800
D. 9x + 2y ¡Ü 1,800
1) The objective function represents the total income generated from selling the mixtures. Since we want to maximize income, the objective function would be the sum of the prices of each box sold, which is given by:
D. 2.8x + 4y
2) The merchant has 1,800 ounces of raisins available, so the total amount of raisins used in the mixtures cannot exceed this quantity. Since mixture A contains 2 ounces of raisins per box and mixture B contains 4 ounces of raisins per box, the inequality representing the constraint is:
A. 2x + 4y ≤ 1,800