Question

b. Reformulate the linear programming model if the company is now interested in maximizing their profit (price raw material cost from dog food production. Assume that Puppy Band so for $9.50 per bag, Adun Blend sells for $8.50 per bag, and Geriatric Blend sells for $9.00 per bag. Further, Chicken costs $2.50 per pound. Fish Meal costs $1.25 per pound, and Soy Flour costs $2.00 per pound. How does this new information change your linear programming model? The new objective function: Maximize Z X X , X, (Enter your responses rounded to two decimal places Enter your answer in the edit fields and then click Check Answer

Answer 1

Answer a= X1= number of 5 lb bags of puppy blend produced

X2=        number of 5 lb bags of adult blend produced

X3= number of 5 lb bags of geriatric blend produced

Objective function= It is to maximize the production

Max Z= X1+X2+X3

Subjected to=

Demand for puppy blend = X1≤2000

Demand for adult blend = X2≤8000

Demand for geriatric blend = X3≤1000

Chicken availability =2.5 X1+1.5X2+X3 ≤10000

Fish availability = X1+2 X2+2 X3 ≤20000

Soya flour availability =0.5 X1+0.5 X2+X3 ≤5000

Answer 2 b= The new objective function wil be to maximize the prfit earned from the production of all three products

Maximize: z = 9.5x1 + 8.5x2 + 9x3-2.5 (2.5x1 + 1.5x2 + x3) -1.5 (x1 + 2x2 + 2x3) -2 (0.5x1 + 0.5x2 + x3)

where

the amount of chicken used to prepare all dog food bags =(2.5x1 + 1.5x2 + x3)

the amount of fish meal used to prepare all dog food bag= (x1 + 2x2 + 2x3) is

the amount of soy flour used to prepare all dog food bags =(0.5x1 + 0.5x2 + x3)

Maximize: z = (9.5 - 2.5*2.5 - 1.5*1 - 2*0.5) *1 +( 8.5 - 2.5*1.5 - 1.5*2 - 2 *0.5) *2 +( 9 - 2.5*1 - 1.5*2 - 2 *1) *3

Maximize: z = 0.75 x1 - 1.25 x2 + 1.5 x3