Practice Exercise Graphical Solution Method Dr. Clara M. Novoa 1. In the Ma-and-

Question

Practice Exercise Graphical Solution Method Dr. Clara M. Novoa 1. 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 ft. A box of Grano occupies 0.2 ft and a box of Wheatie needs 0.4 ft. The maximum daily demands of grano and Wheatie are 200 and 120 boxes, respectively. A box ofGrano nets$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% of the total square feet to Wheatie and 43% to Grano. a. Formulate the LP problem using the spaces in the table below b. Find the optimal solution graphically (use the graph paper in page 3) c. Compare the optimal solution to the assignments Ma and-Pa plans to do. Are Ma-and-Pa assignments better than the optimal solution you found? Fill out tables in page 4. objective Function (2%): Decision Variables (4%): maximize total profit number of boxes of coch cereal it 1.3s x2 How many of erano box X2 How many of Wneonhe boxes sign constraints (2%): Constraints (12%): X, 20 x S 20 o. 2 x t o. 4 x 2 Coo

Explanation / Answer

optimal Solution

Consider 2 inequalities at one time and convert them into equalitites,

0.2x1+0.4x2=60

x1 = 0

x2 = 150

Solution : ( 0 , 150)

Now consider

0.2x1+0.4x2=60

with

x2 = 0

x1=200

x2=120

we get solutions as (300,0) , (200,50) and (60,120) respectively.

Ignoring 1 and 2 as they are above the maximumm demand

the values of z on these points is 267.5 and 222 respectively.

So z is maximum at point (200,50) which makes it the optimal solution

In conclusion, Ma- and- Pa grocery store should have 200 boxes of Grano and 50 boxes of wheatie

Sq. ft / box Box profit/box Total Profit Wheatie 0.4 85.5=85 1.3 110.5 Grano 0.2 129 1 129 Total 0.28 214 1.12 239.5

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