Set 16: Linear Inequalities

Choice A is correct. Choice A is the correct answer. Profit is calculated as Revenue minus Costs. 1. Revenue: $$25per cake ($25 c) 2. Variable Cost: \8per cake (8 c$$) 3. Fixed Cost: \$$600rent 4. Profit Equation: Profit = Revenue - Variable Cost - Fixed Cost 5. Inequality: $$(25 c - 8 c) - 600 \geq 1000 6. Simplify: $17c - 600 \geq 1000$ 7. Add 600: $17c \geq 1600$ 8. Divide by 17: $c \geq 94.11...$ 9. Round up: Since you can't sell a fraction of a cake, $c \geq 95$ Strategic Tip: Net profit per unit is (Selling Price - Cost per unit). Total Profit = (Net per unit × Quantity) - Fixed Costs. Choice B is incorrect because it ignores the variable cost of ingredients ($25c - 600 \geq 1000$). Choice C is incorrect because it ignores the rent ($17c \geq 1000$). Choice D is incorrect because while the setup is correct, Choice A is the solved answer, and D is just the setup (though mathematically valid, A is the explicit solution requested by "How many cakes..."). Correction: Choice D is the setup, but A is the solution. The question asks "How many cakes", so A is the answer.