Question

Weez All Nuts, Inc. determined that their cocktail nut mix should have the following minimum requirements in the 1 lb. can they sell for $3.99. At least 10% Brazil nuts. Brazil nuts cost $2.50 a pound. A maximum of 50% pecans at $1.40 a pound. At least 20% pistachios at $2.25 a pound, A maximum of 40% cashews at $2.00 a pound. The can costs $0.10 Find the proportion of these nuts by weight to maximize profit. What is the profit that will be made per can if it is sold at a retail store for $3.00 a can.

Answer 1

LP model:

Decision variables: Let a,b,c,d represent the lbs of brazil nuts, pecans, pistachios, and cashews used respectively in 1 lb of the cocktail nut mix.
constraints:
a,b,c,d>=0	non negativity
a>=10%(a+b+c+d)	Brazil nuts
b<=50%(a+b+c+d)	pecans
c>=20%(a+b+c+d)	pistachios
d<=40%(a+b+c+d)	cashews
(a+b+c+d)=1	total weight
Objective Function:
Maximize Profit
Profit = [3.99(a+b+c+d)]-[2.50a+1.40b+2.25c+2d+0.10]

excel model:

solver solution:

What is the profit that will be made per can if it is sold at a retail store for $3.00 a can:

What is the profit that will be made per can if it is sold at a retail store for $3.00 a can.

if the price is $3.00 a can Profit per can = $1.10