. Input the Restaurant menu problem into your generic linearprogramming spreadsheet and confirm the solution given (or prove itwrong).

How Do Restaurants Use Linear Programming for Menu Planning?

Linear algebra helps restaurants earn a profit.

Restaurants use linear programming for menu planning. It usesbasic algebra to optimize meal production and thereby increaserestaurant profits. Linear algebra reflects a direct relationshipbetween an increase or decrease in food resources, and an increaseor decrease in meal production. For example, if the kitchen hasonly half its needed supply of cream base, then it can only preparehalf its normal amount of cream soups. Additionally, management candetermine the cost of preparing different menu items to decide howmany of each menu item to prepare for optimal profit.

Weekly Meal Planner

Step 1

Choose the decision variables that apply. In this example, arestaurant needs to produce 250 of its dinner specials per day, onewith meat and the other vegetarian. The decision variables are thenumber of meals and the different menu names (i.e., porterhousesteak and spinach lasagna).

Step 2

Choose the objective for the restaurant. Normally, the objectiveis to determine how many of each menu item to prepare that meetsthe required number of meals yet stays within budget, so this isthe objective for the example shown. However, the objective will bethe quantity of physical supplies on hand, if there is a shortageof a particular ingredient that several menu items use, such astomato sauce. Then management can determine how to get the largestnumber of meals with the quantity of tomato sauce on hand.

Step 3

Choose the constraints on menu production, which is the day’smonetary budget to produce a specified number of meals. Forexample, a restaurant has a $1,000 budget for that day’s two dinnerspecials, and it must prepare 250 meals that cost different amountsto prepare. It cannot spend more than $1,000 and still earn aprofit.

Step 4

Choose the two dinner specials, such as porterhouse steak andspinach lasagna. For this example, the porterhouse steak costs $7to prepare and the lasagna dinner costs $3. The steak is designatedas “S” and the lasagna as “L."

Step 5

Calculate how many steak dinners the restaurant can prepare for$1,000: S + L = 250 meals. 7S <= $1,000 S <= $1,000 / 7 =142.85 S = 142 meals for $1,000 (The restaurant cannot serve 85/100of a meal, so that amount is dropped.)

Step 6

Calculate how many lasagna dinners the restaurant can preparefor $1,000. 3L <= $1,000 L <= $1,000 / 3 = 333.33 L = 333meals for $1,000

Step 7

Calculate the ratio: 142S divided by 333L = 42 percent (drop thedecimals). This means that 42 percent of the meals should be steakdinners. Conversely, 58 percent of the dinner specials should bespinach lasagna.

Step 8

Calculate the number of steak dinners the restaurant can prepareon its budget: 142S times 42 percent = 59 steak dinners (drop thedecimals)

Step 9

Calculate the number of spinach lasagna dinners the restaurantcan prepare on its budget: 333L times 58 percent = 193 lasagnadinners.

Step 10

Verify the quantity of meals: 59 steak dinners plus 193 lasagnadinners = 252 meals. Since the restaurant only has to prepare 250meals, it is under budget, which means increased profit.

Step 11

Verify the cost: 59 steak dinners times $7 equals $413. 193lasagna dinners times $3 equals $579. $413 + $579 = $992, which isunder budget.