What is the cheapest menu that still keeps every promise?

A hundred and twenty guests at 1.25 servings each, six dishes, and three promises: enough food, at least 55 vegetarian servings, at least 90 hot ones. Twenty-five servings of everything costs $560. The optimizer feeds the same room for $490.80.

Operations Starter Optimization free

After you install, this is the model to open.

Feed Everyone for the Least Money

  1. In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
  2. Click Start from a template and put that name in the search box.
  3. Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.

The answer

An even spread against the optimized menu:

Optimized cost
$490.80 $4.09 a guest
Even spread
$560.00 25 servings of everything
Saving
$69.20 12%
The answer
54 + 48 curry and salad, four at the minimum

You can read the reasoning off the answer: salad is the cheapest thing on the sheet so it takes as much of the cold requirement as it can, and vegetable curry is the cheapest hot dish so it carries the hot promise as far as the share rule allows. The twelve-serving floors are doing more work than they look, because the two meat dishes are only on the menu at all because a tray is a tray. Raise the vegetarian minimum to 90 servings and the cost barely moves, since the cheap dishes were already the vegetarian ones. What the sheet cannot tell you is whether the room will eat the curry.

The model

One row per dish with its cost a serving and flags for hot and vegetarian. Two rules make the answer less obvious than it looks: nothing can be ordered in fewer than twelve servings, and no dish may carry more than 40 percent of the menu.

Guests / servings120 / 150
Dishes6, $2.80 to $6.20 a serving
Vegetarian / hot minimum55 / 90 servings
Tray minimum, share ceiling12 servings, 40%
Food costsolved

Once it is in your sheet

  1. The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
  2. Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
  3. Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.

Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.