# Thread: Linear Programming Problem unsolved.

1. ## Linear Programming Problem unsolved.

Help me solve this linear programming problem. Can't decide whether it's a maximization/minimization problem?

In the J & K 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 79ft^2. A box of Grano occupies 0.2ft^2 and a box of Wheatie needs 0.4ft^2. The maximum daily demands of Grano and Wheatie are 280 and 127 boxes, respectively. A box of Grano nets $1.00 in profit and a box of Wheatie$1.47.

J & K thinks that because the unit profit of Wheatie is 47% higher than of Grano, Wheatie should be allocated 47% more space than Grano, which amounts to allocating about 73.5% to Wheatie and 26.5% to Grano.

Can someone help me formulate the LP model for this one? I've been trying for days. I need the answer by tmrw. Please help.

Thanks a million.

2. Originally Posted by Sher
Help me solve this linear programming problem. Can't decide whether it's a maximization/minimization problem?

In the J & K 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 79ft^2. A box of Grano occupies 0.2ft^2 and a box of Wheatie needs 0.4ft^2. The maximum daily demands of Grano and Wheatie are 280 and 127 boxes, respectively. A box of Grano nets $1.00 in profit and a box of Wheatie$1.47.
Let x = no. boxes of Grano
Let y = no. boxes of Wheatie

1st constraint is shelf space

.2x + .4y <= 79

2nd and 3rd constraints deal with daily demand

0 <= x <= 280

0 <= y <= 127

The profit function is

P = 1x + 1.47y

Originally Posted by Sher
J & K thinks that because the unit profit of Wheatie is 47% higher than of Grano, Wheatie should be allocated 47% more space than Grano, which amounts to allocating about 73.5% to Wheatie and 26.5% to Grano.
I ignored what J & K thought and graphed the constraints to find the feasible region. The region had vertices at

(141, 127), (280, 57.5), (280, 0), (0, 0)

Use these to find the maximum profit in the profit function.