Question

1. Consider an LP where you have to determine how much/many of each product to manufacture; there in all, TWO products made from three ingredients. The ingredient usage matrix is as follows. Ingredint1 ingredint2 ingredient3 Product1 1 5 2.5 Product2 4 3 3 Prices of products 1, and 2 are respectively, $65, $55 per unit. Prices of ingredients are respectively, $5, $2 and $4 per unit. You have to formulate an LP to maximize net profit. Product 1 cannot exceed 100 units; ingredient 2 cannot exceed 80 units in consumption.

(a) Define variables (10 points) (You will use these variables for (b)-(d))

(b) Write the objective function. (15)

(c) Write the constraint on the amount of product 1. (10)

(d) Write the constraint ensuring that you do not plan on using more of ingredient 2 than you have available.

Answer 1

a)

Decision variable => xi = number of units to produce for product i where i ={1,2}

b)
Per unit profit for product 1 => 65-1*5-5*2-2.5*4 = 40
Per unit profit for product 2 => 55-4*5-3*2-3*4 = 17

Objective function is to maximize profit = max 40x1+17x2

c)

Constraint for product 1 => x1 <= 100
d) Constraint for ingredient 2 => 5x1+3x2 <= 80

Solving in solver we get,

X1 = 16, X2 = 0 and maximized profit = 640

Solver screenshot

Solver formula

Solver window