Answer:
- total costs = 0.93n +220
- revenue = 2.90n
- profit = 1.97n -220
- cost for 320 bags: $517.60
- revenue for 320 bags: $928
- profit for 320 bags: $410.40
Explanation:
Given that bags of peanuts cost $0.93 each, booth rental costs $220 for the week, and your selling price is $2.90 per bag, you want expressions for cost, revenue, and profit, and you want these values when sales are 320 bags of peanuts for the week.
Cost
The total cost is the sum of fixed and variable costs. The fixed cost is the cost of booth rental, $220. The variable cost is the per-bag cost of peanuts, multiplied by the number of bags.
total cost = 0.93n +220
Revenue
The revenue is the selling price, multiplied by the number of bags sold:
revenue = 2.90n
Profit
Profit is the difference between revenue and cost.
profit = revenue -cost
profit = (2.90n) -(0.93n +220)
profit = 1.97n -220
320 bags sold
cost = 0.93·320 +220 = 297.60 +220 = $517.60 . . . total costs
revenue = 2.90·320 = $928.00 . . . revenue
profit = 1.97·320 -220 = 630.40 -220 = $410.40 . . . profit
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Additional comment
The attached graph shows the cost (red), revenue (green), and profit (blue) curves. The vertical line identifies the values of these for 320 units sold.
It takes sales of 112 bags to pay the costs (break even).
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