George is planning to have a one-day stand at the Boy Scout event. He is plannin

Question

George is planning to have a one-day stand at the Boy Scout event. He is planning to sell his entire inventory by the end of the day. He has 200 cans of lemonade, 300 cans of Coke, 400 small bottles of Coke. Each can cost him 50 cents. He wants to sell at least 100 lemonade and 200 Coke Cans. The cost of renting the stand for one-day is $100. He wants to price lemonade at $1 each, coke can at $1.5 and bottles at $2. Using Excel Solver calculate the number of individual items he should attempt to sell to maximize his profit. (Note: Include the rental cost in the price of the individual items) can you plese show your work using excel and solver and explain your answer thanks.

Explanation / Answer

let x be the number of lemonade cans sold, y be the number coke cans sold and z be the number of small coke bottles sold.

As per given condition, x <= 200, y <=300 and z <= 400 (This is the supply condition)

Cost price of all cans = 0.5x + 0.5y + 0.5z

Selling price of all cans = x + 1.5y + 2z

Rent cost = 100

Profit = x + 1.5y + 2z - (0.5x + 0.5y + 0.5z) - 100 = 0.5x + y + 1.5z - 100

Hence LPP can be formulated as,

Maximize Z = 0.5x + y + 1.5z - 100

subject to,

x <= 200, y <= 300 and z<=400

Below is the solver solution

Hence maximum profit will be acheived when all the available inventory will be sold. And profit will be $900

Solver Solution x y z Total Demand Decision Variables 200 300 400 Profit 0.5 1 1.5 900 Constraint 1 1 0 0 200 200 Constraint 2 0 1 0 300 300 Constraint 3 0 0 1 400 400

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