Bark's Pet Company produces canned cat food caled Meow Chow and canned dog food called Bow Chow. The company produces the pet food by blending horse meat, ground fish, and a cereal additive. Each week the company has 600 pounds of horse meat, 800 pounds of ground fish, and 1,000 pounds of cereal additive available to produce both kinds of pet food. Meow Chow must be at least half fish, and Bow Chow must be at least half horse meat. The company has 2,350 one pound cans available each week. A can of Meow Chow earns $1.10 in profit, and a can of Bow Chow earns $1.40in profit. The company wants to maximize its weekly profit using excel, what are some of these formulas?

Refer explanation for the answer and calculations

Step-by-step explanation

Let,

xij = pound of ingredient i in cat food j where i = {horse meat = 1,ground fish=2,cereal additive=3} and j = {meow Chow=1,Bow Chow=2}

Objective is to maximize profit = Max 1.1*(x11+x21+x31)+1.4*(x12+x22+x32)

subject to,

x11+x12 <= 600 (Horse meat)

x21+X22 <= 800 (Ground Fish)

x31+x32 <= 1000 (Cereal additive)

x11+x21+x31+x12+x22+x32 <= 2350 (Total number of cans)

x21 >= 0.5*(x11+x21+x31) (Meow chow is At least half fish)

or, -0.5x11+0.5x21-0.5x31 >= 0

x12 >= 0.5*(x12+x22+x32) (Bow Chow must be at least half horse meat)

or, 0.5x12-0.5x22-0.5x32 >= 0

xij >= 0 (non-negativity constraint)

Solving in solver we get,

Meow Chow:

Horse Meat = 0

Ground Fish = 800

Cereal additive = 350

Bow Chow:

Horse Meat = 600

Ground Fish = 0

Cereal additive = 600

Maximized weekly profit = $2,945

please see the attached file for the complete solution.