Question

a bakery has bought 140 lbs of muffin dough. They want to make muffins and waffles in half dozen packs out of it. A pack of muffins requires one pound of dough & a pack of waffles requires half a pound of dough. It takes bakers 2 minutes to make a half dozen of muffins & 5 minutes to make a half dozen of waffles. The bakery make $1.50 profit on each pack of muffins and $2.00 profit on each pack of waffles. What is the max possible profit the bakery can make from the muffin dough it purchased if the bakers need to complete the baking in 10 hours or less (600 minutes)?

a)$210 b)$240 c)$310 d) $320 e)none

Answer 1

This is a Linear Programming problem

If there are x₁ packs of waffles and x₂ packs of muffins,we have to

subject to

Using graphical method , we get

To draw constraint 0.5 + ≤ 140→(1)
  
Treat it as 0.5 + =140

When = 0 then = ?

⇒0.5(0) +​​​​​​​ = 140

⇒​​​​​​​ = 140

When x2 = 0 then = ?

⇒0.5 + (0)=140

⇒0.5 = 140

⇒ = 140 / 0.5 = 280

	0	280
​​​​​​​	140	0

Treat it as 5 + 2​​​​​​​ = 600

When = 0 then ​​​​​​​= ?

⇒5(0) + 2​​​​​​​=600

⇒2​​​​​​​ = 600

⇒​​​​​​​ = 600 / 2 = 300

When ​​​​​​​ = 0 then =?

⇒5 + 2(0) = 600

⇒5 = 600

⇒ = 600 / 5 = 120

	0	120
​​​​​​​	300	0

The value of the objective function at each of these extreme points is as follows:

The value of the objective function at each of these extreme points is as follows:

Extreme Point Coordinates (,)	Objective function value z = 1.5 + 2
O(0,0)	1.5(0)+2(0)=0
A(120,0)	1.5(120)+2(0)=180
B(80,100)	1.5(80)+2(100)=320
C(0,140)	1.5(0)+2(140)=280

The maximum value of the objective function z=320 occurs at the extreme point (80,100).

Hence, the optimal solution to the given LP problem is : = 80 , = 100 and max z=320

Answer : d) $320