In the Ma-and-Pa grocery store, shelf-space is limited and must be used effectively to increase profit. Two-cereal items, Grano

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In the Ma-and-Pa grocery store, shelf-space is limited and must be used effectively to increase profit. Two-cereal items, Grano

and Wheatie, compete for a total shelf space of 60 ft2 . A box of Grano occupies .2ft2 and a box of Wheatie needs .4ft2 . The maximum daily demands of Grano and Wheatie are 200 and 120 boxes, respectively. A box of Grano nets in $1.00 in profit and a box of Wheatie $1.35. Ma-and-Pa thinks that because the unit profit of Wheatie is 35% higher than that of Grano, Wheatie should be allocated 35% more space than Grano, which amounts to allocating about 57% to Wheatie and 43% to Grano. What do you think?

Mathematics

1 answer:

Inessa [12.5K] · Answer 1 · 2026-03-19T23:18:20+03:00

No. Allocate 2/3 of the space to Grano and 1/3 to Wheatie. This results in approximately 57% for Wheatie and 43% for Grano—meaning 60(.57)=34.2 ft² for Wheatie and 60(.43)=25.8 ft² for Grano. Therefore, there would be about 85.5 boxes of Wheatie and 129 boxes of Grano, leading to a total profit of 129(1)+85(1.35)=$243.75. The best choice would be to place 200 boxes of Grano and 50 boxes of Wheaties on the shelf. Allocating 40 ft² to Granos (200(.2)) and 20 ft² to Wheaties (50(.4)) means that 40/60=2/3=66.6% of the space would be for Granos, and 20/60=1/3=33.3% would be for Wheaties. The total profit would be 200(1)+50(1.35)=$267.5.

In the Ma-and-Pa grocery store, shelf-space is limited and must be used effectively to increase profit. Two-cereal items, Grano

- 128 Superscript StartFraction 3 Over x EndFraction

- (4RootIndex 3 StartRoot 2 EndRoot)x

- (4 (2 Superscript one-third Baseline) ) Superscript x

Step-by-step explanation: