Question

The Health Fare Cereal Company makes three cereals using wheat, oats, and raisins. The portions and profit of each cereal are the following: Portion of Each Pound of Cereal Cereal Lite Trim Health Fare wheat Oats Raisins Profit/Pound 0.75 0.25 0 $0.75 0.50 0.25 0.25 $0.75 0.25 0.50 0.25 $0.96 The company has 2320 pounds of wheat, 1380 pounds of oats, and 700 pounds of raisins available. How many pounds of each cereal should it produce to maximize profit? Lite Trim Health Fare profit

Answer 1

Pls, give thumbs up.

Let x1= company produces of Lite

Let x2= company produces of Trim

Let x3= company produces of Health Fare

The LPP maximization problem is given as

MAX z = 0.75x1 + 0.75x2 + 0.96x3
subject to
0.75x1 + 0.5x2 + 0.25x3 <= 2320
0.25x1 + 0.25x2 + 0.5x3 <= 1380
0.25x2 + 0.25x3 <= 700
and x1,x2,x3 >= 0

Solving using excel we get,

Lite=1600

Trim=1680

Health Fare=1120

Profit=3535.2

Variables: Lite Trim Health Fare 1680 1120 1600 Objective Function: Lite Max Trim Health Fare 0.75 0.96 0.75 Constraints: Lite Trim 0.75 0.25 0 0.5 0.25 0.25 Health Fare 0.25 0.5 0.25 Inequality R.H.S 2320 <= 2320 1380 <= 1380 700 <= 700 Profit: 3535.2

Solver Parameters Set Objective: $B$16 TO: O Max O Min O Value of: By Changing Variable Cells: $B$3:$D$3 Subject to the Constraints: $E$11:$E$13 <= $G$11:$G$13 Add Change Delete Reset All Load/Save ✓ Make Unconstrained variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Formulas:

for E27 A C D G H Variables: Lite Trim Health Fare 1680 1120 1600 oo vanewno 5 Objective Function: Lite 7 Max Trim Health Fare 0.75 0.96 0.75 9 Constraints: Lite Trim 0.75 0.25 0 Health Fare 0.5 0.25 =B11*B3+C11*C3+D11*D3 0.25 0.5 =B12*B3+C12*C3+D12*D3 0.25 0.25 =B13*B3+C13*C3+D13*D3 Inequality R.H.S 2320 1380 700 16 Profit: =B7*B3+C7*C3+D7*D3