Variables and Constraint Equations Each variable in our linear program represent
ID: 362737 • Letter: V
Question
Variables and Constraint Equations Each variable in our linear program represents the quantity of each item that is available for distribution every month. The total price of the food items is constrained by the budget, which is our first constraint e Every month, "Food for All" uses about $1800 to purchase food. According to the director of the company, every week the budget is S450, and last year as a whole, "Food for All used $23,400 Using the food order list from last month and the price that we collected, we calculated that total price of all the food available at last month's pantry is $2000.00 before discount. With the exact same price, items and availability constraints we want to see what combination of refreshments and snacks can we prepare for our care packages each week. Respectively, for each refreshment they sell for S0.25 and snacks sell for S0.50. We believe we should buy no more than 900 Refreshments and 500 Snacks. How should we evenly split the groceries per week?Explanation / Answer
Last months' total price of all food available is given as $2,000.
Every week budget is restricted to $450.
Decision variables arecombinations of refreshments and snacks per week. Let R represents refreshments and S number of snacks.
Price for refreshment is 0.25 whereas price of snack is 0.50.
Budgetary constraint 0.25R + 0.50S <= 450
Quantity constraints are R <= 900 and S <= 500
Question asked is: How should we evenly split the groceries per week?
In case it is about spliting the budget evenly, then $225 for refreshments and $225 for snacks provide R=900 and S=450
Objective function may be Maximize .25R - .50S or Minimize .50S - .25R
Formulation and solution using excel solver is as follows:
Decision Variables R S SumProduct Values of DV 900 450 Objective Minimization -0.25 0.5 0 Constraints LHS Sign RHS Budget weekly 0.25 0.5 450 "= 450 No.Refreshments 1 0 900 <= 900 No. of Snacks 0 1 450 <= 500Related Questions
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