Profit Practice Find the profit function and the breakeven point for each problem below. HINT: The quadratic formula and / or a tech tool helps. 2. Managers at a restaurant estimate that, to sell x sandwiches each day, the price of a sandwich should be D(x) = 15.75 - 15x. The cost of making x sandwiches is C(x) = 260 + 3.15x.-
Added by Fernando G.
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Given \( D(x) = 15.75 - 15x \), the revenue function is: \[ R(x) = x \cdot D(x) = x(15.75 - 15x) = 15.75x - 15x^2 \] Show more…
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You've decided to go into business making personal pizzas. Answer the following questions given x is the number of pizzas you sell (in hundreds) and p is the price in dollars. The demand equation for pizzas is given by p = 25 - x The cost equation for producing pizzas is C(x) = 109.25 + 4x a) Find R(x), the revenue obtained from selling x pizzas. R(x) = [ Select ] b) Find P(x), the profit obtained from selling x pizzas, and simplify. P(x) = [ Select ] c) Find the Break-Even point(s) for P(x). x = [ Select ] d) Find the vertex of P(x) using Calculus or the formula. vertex = [ Select ] e) Find the Marginal Profit at a production level of 1000 pizzas. Marginal Profit = $ [ Select ] f) The answer from part (e) tells us that increasing x by one at a production level of 1000 pizzas will [ Select ] profit.
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A restaurant sells x hamburger per week. Assume that the weekly cost and demand equations C(x) = 1.1x + 300 p(x) = 5 - 0.03x 0 ≤ x ≤ 1,000 Find the number of hamburgers that the restaurant should sell and the price that the restaurant should charge for each hamburger to maximize the profit.
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We saw that the profit, $P(x),$ generated after producing and selling x units of a product is given by the function $$P(x)=R(x)-C(x)$$, where $R$ and $C$ are the revenue and cost functions, respectively. Use these functions to solve. Hunky Beef, a local sandwich store, has a fixed weekly cost of $\$ 525.00,$ and variable costs for making a roast beef sandwich are $\$ 0.55$. a. Let $x$ represent the number of roast beef sandwiches made and sold each week. Write the weekly cost function, $C,$ for Hunky Beef. b. The function $R(x)=-0.001 x^{2}+3 x$ describes the money that Hunky Beef takes in each week from the sale of $x$ roast beef sandwiches. Use this revenue function and the cost function from part (a) to write the store's weekly profit function, $P$. c. Use the store's profit function to determine the number of roast beef sandwiches it should make and sell each week to maximize profit. What is the maximum weekly profit?
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