Question

tamera is buying rectangular planters for her garden. she can choose between a small planter and a large planter. the small planter costs $25, can hold four plants, and takes up five square feet of ground space. the large planter costs $35, can hold six plants, and takes up 15 square feet of ground space. tamera needs to plant at least 180 plants and her garden only has 300 square feet of ground space available for the planters. how many of each type of planter should tamera buy to minimize her cost? a. 60 small planters and 0 large planters b. 10 small planters and 30 large planters c. 30 small planters and 10 large planters d. 45 small planters and 0 large planters

Explanation:

Step1: Check Plant Requirement

For each option, calculate total plants:

• A: \(60\times4 + 0\times6 = 240\) (≥180)
• B: \(10\times4 + 30\times6 = 40 + 180 = 220\) (≥180)
• C: \(30\times4 + 10\times6 = 120 + 60 = 180\) (≥180)
• D: \(45\times4 + 0\times6 = 180\) (≥180)

Step2: Check Space Requirement

• A: \(60\times5 + 0\times15 = 300\) (≤300)
• B: \(10\times5 + 30\times15 = 50 + 450 = 500\) (>300, invalid)
• C: \(30\times5 + 10\times15 = 150 + 150 = 300\) (≤300)
• D: \(45\times5 + 0\times15 = 225\) (≤300)

Step3: Calculate Cost

• A: \(60\times25 + 0\times35 = 1500\)
• C: \(30\times25 + 10\times35 = 750 + 350 = 1100\)
• D: \(45\times25 + 0\times35 = 1125\)

Compare costs: 1100 (C) < 1125 (D) < 1500 (A). So C has lowest cost.

Answer:

C. 30 small planters and 10 large planters