Choosing a Farmers Market Booth Contract
A baker sells at a weekly farmers market on both Wednesdays and Saturdays. The market offers two booth contracts. Option A charges $45 per market day plus 6% of that day's sales. Option B charges a flat $95 per market day with no percentage. Last season she sold about $1,150 on each of four Saturdays and about $540 on each of four Wednesdays, and she is committed to exactly those eight days this season. The market permits her to choose a different contract for Wednesday than for Saturday. Her cousin argues that because her average daily sales are $845, which is above the break-even point, she should simply take Option B every day and stop thinking about it. The baker is uneasy: she remembers that a single rainy Saturday two years ago cut her sales to about $600, and she wants a rule she can apply day by day rather than to a season average.
1. Find the daily sales amount at which the two options cost the same, and explain what the 0.06 in Option A represents.
Read the worked answer
Let s be one day's sales in dollars.
Option A cost = 45 + 0.06s; Option B cost = 95.
45 + 0.06s = 95 → 0.06s = 50 → s = $833.33.
Below $833.33 in daily sales, Option A is cheaper; above it, Option B is cheaper. The 0.06 is a marginal rate: every additional dollar of sales adds $0.06 to the Option A bill while the Option B bill stays fixed at $95, so B's advantage grows by 6 cents per dollar of sales past the break-even point.
2. Compute the season total under (a) Option A on all eight days, (b) Option B on all eight days, and (c) the best possible mix. Which is cheapest and by how much?
Read the worked answer
Total sales = 4($1,150) + 4($540) = $4,600 + $2,160 = $6,760.
- (a) All A: 8($45) + 0.06($6,760) = $360 + $405.60 = $765.60
- (b) All B: 8($95) = $760.00
- (c) Best mix (B on Saturdays, A on Wednesdays): 4($95) + [4($45) + 0.06($2,160)] = $380 + $180 + $129.60 = $689.60
The mix is cheapest, saving $76.00 versus all-A and $70.40 versus all-B. The cousin's rule used the $845 average day, which sits barely above the $833.33 break-even; averaging hides that Saturdays are far above break-even and Wednesdays are far below it, so a single plan applied to both days is worse than either plan applied where it belongs.
3. A rainy Saturday is expected to bring sales down to $600. Does the Saturday choice flip? At what sales level would she be indifferent?
Read the worked answer
At $600 in sales:
- Option B = $95
- Option A = 45 + 0.06(600) = 45 + 36 = $81
Option A is cheaper by $14, so yes, the Saturday choice flips. The indifference point is the same $833.33 computed earlier, because it comes from the same two cost expressions; only the interpretation changes from a season average to a single day.
This is the practical rule she wanted: price the day, not the season. Any day projected below $833.33 in sales should take Option A, and any day above it should take Option B.