Question

mary makes and sells picture frames at craft fairs. she needs to make some picture frames in advance for an upcoming fair. she wants to make two different frame types: wood and iron. it costs mary $4 to make a wood frame and $8 to make an iron frame. she charges $10 for a wood frame and $15 for an iron frame. mary wants to spend no more than $234 making frames and wants to make at least $240 in revenue from frame sales. if it takes mary 20 minutes to make a wood frame and 35 minutes to make an iron frame, then how many wood and iron frames should mary make to minimize the time she spends on the project? a. mary’s time is minimized when she makes 0 wood frames and 26 iron frames. b. mary’s time is minimized when she makes 24 wood frames and 0 iron frames. c. mary’s time is minimized when she makes 0 wood frames and 16 iron frames. d. mary’s time is minimized when she makes 18 wood frames and 4 iron frames.

Explanation:

Step1: Check Cost and Revenue for Each Option

• Option A: Cost = \(0\times4 + 26\times8 = 208\) (≤234), Revenue = \(0\times10 + 26\times15 = 390\) (≥240). Time = \(0\times20 + 26\times35 = 910\) minutes.
• Option B: Cost = \(24\times4 + 0\times8 = 96\) (≤234), Revenue = \(24\times10 + 0\times15 = 240\) (≥240). Time = \(24\times20 + 0\times35 = 480\) minutes.
• Option C: Cost = \(0\times4 + 16\times8 = 128\) (≤234), Revenue = \(0\times10 + 16\times15 = 240\) (≥240). Time = \(0\times20 + 16\times35 = 560\) minutes.
• Option D: Cost = \(18\times4 + 4\times8 = 72 + 32 = 104\) (≤234), Revenue = \(18\times10 + 4\times15 = 180 + 60 = 240\) (≥240). Time = \(18\times20 + 4\times35 = 360 + 140 = 500\) minutes.

Step2: Compare Times

Compare the times: 480 (Option B) < 500 (Option D) < 560 (Option C) < 910 (Option A).

Answer:

B. Mary’s time is minimized when she makes 24 wood frames and 0 iron frames.