Question

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?

Answer 1

Answer:

No. 2/3 of the space to Grano and 1/3 of the space to Wheatie.

Step-by-step explanation:

Allocating about 57% to Wheatie and 43% to Grano, means to allocate 60(.57)=34.2 ft2 of Wheatie and 60(.43)=25.8 ft2 of Grano. In that case there would be 34.2/.4=85.5≈85 boxes of Wheatie and 25.8/.2=129 boxes of Grano. The total profit would be 129(1)+85(1.35)=$243.75

Best option:

200 Granos boxes and 50 Wheaties boxes on the shelf.

200(.2)=40ft^2 will allocate Granos boxes

50(.4)=20ft^2 will allocate Wheaties boxes.

This means that 40/60=2/3=66.6% of the space will allocate Granos boxes and 20/60=1/3=33.3% of the space will allocate Wheaties boxes.

The total profit would be 200(1)+50(1.35)=$267.5

EXTRA:

This is a optimization problem.

Let X1 be the number of Granos boxes

Let X2 be the number of Wheaties boxes

Objective:

Max Z=1(X1)+1.35(X2)

Subjecto to

0.2(X1)+0.4(X2)<=60,

X1<=200,

X2<=120,

X1,X2>=0.

You can solve it using the simplex method. Check the image for more details.