The manager of a restaurant found that the cost to produce $100$ cups of coffee is $\$11.02$, while the cost to produce $400$ cups is $\$40.12$. Assume the cost is a linear function of $x$, the number of cups produced. $a.$ Find a formula for $C(x)$. $b.$ What is the fixed cost? $c.$ Find the total cost of producing $1000$ cups. $d.$ Find the total cost of producing $1001$ cups. $e.$ Find the marginal cost of the $1001$st cup. $f.$ What is the marginal cost of any cup and what does this mean to the manager?

The manager of a restaurant found that the cost to produce 100 cups of coffee is 11.02 dollars, while the cost to produce 400 cups is 40.12 dollars. Assume the cost C(x) is a linear function of x, the number of cups produced.

What is the marginal cost of any cup and what does this mean to the manager?

Suppose that the demand and price for a certain model of a youth wristwatch are related by $p=D(q)=16-1.25 q$, where $p$ is the price (in dollars) and $q$ is the quantity demanded (in hundreds). Find the price at each level of demand.

a.0 watches
b.400 watches
c. 800 watches

Find the quantity demanded for the watch at each price.

d. $8
e.$10
f. $12 g. Graph$p=16-1.25 q$.

Suppose the price and supply of the watch are related by$p=S(q)=0.75 q$, where$p$is the price (in dollars) and$q$is the quantity supplied (in hundreds) of watches. Find the quantity supplied at each price.

h.$0
i. $10
j.$20
k. Graph $p=0.75 q$ on the same axis used for part $g$.
l. Find the equilibrium quantity and the equilibrium price.

A farmer buys a new tractor for $157,000 and assumes that it will have a trade-in value of$82,000 after 10 years. The farmer uses a constant rate of depreciation (commonly called straight-line depreciation-one of several methods permitted by the IRS) to determine the annual value of the tractor.

(A) Find a linear model for the depreciated value V of the tractor t years after it was purchased.

(B) What is the depreciated value of the tractor after 6 years?

(C) When will the depreciated value fall below $70,000?

(D) Graph V for$0 \leq t \leq 20$ and illustrate the answers from parts (B) and (C) on the graph.

You are the manager of a firm. You are considering the manufacture of a new product, so you ask the accounting department for cost estimates and the sales department for sales estimates. After you receive the data, you must decide whether to go ahead with production of the new product. Analyze the data in below problem (find a break-even quantity) and then decide what you would do in each case. Also write the profit function. $C(x)=85 x+900 ; R(x)=105 x$;no more than $38$ units can be sold.

The manager of a restaurant found that the cost to produce 100 cups of coffee is 11.02 dollars, while the cost to produce 400 cups is 40.12 dollars. Assume the cost C(x) is a linear function of x, the number of cups produced.

Find a formula for C(x).

A company produces two types of steel. Type 1 requires 2 hours of melting, 4 hours of cutting, and 10 hours of rolling per ton. Type 2 requires 5 hours of melting, 1 hour of cutting, and 5 hours of rolling per ton. Forty hours are available for melting, 20 for cutting, and 60 for rolling. Each ton of Type 1 produces $240 profit, and each ton of Type 2 yields$80 profit. Find the maximum profit and the production schedule that will produce this profit.

Let $C(x)$ be the cost to produce $x$ batches of widgets, and let $R(x)$ be the revenue in thousands of dollars. For each exercise, (a) graph both functions, (b) find the minimum break-even quantity, (c) find the maximum revenue, and (d) find the maximum profit.

$$R(x)=-4 x^{2}+36 x, \quad C(x)=16 x+24$$

Suppose a demand function is given by $q=D(p)=30\left(5-\frac{p}{\sqrt{p^{2}+1}}\right)$, where $q$ is the demand for a product and p is the price per item in dollars. Find the rate of change in the demand for the product per unit change in price $($ i.e., find $d q / d p)$.

What is the conversion cost to manufacture insulated travel cups if the costs are: direct materials, $17,000; direct labor,$33,000; and manufacturing overhead, $70,000? A.$16,000 B. $50,000 C.$103,000 D. $120,000

Business The manager of a 200-unit apartment complex has found that the profit is given by

$$P=x^2+300 x-18,000,$$

where x is the number of apartments rented. For what values of x does the complex produce a profit?

Suppose that the demand and price for strawberries are related by $p=D(q)=5-0.25 q$, where $p$ is the price (in dollars) and $q$ is the quantity demanded (in hundreds of quarts). Find the price at each level of demand. $a.\ 0$ quarts $\quad b.\ 400$ quarts $\quad c.\ 840$ quarts

Find the quantity demanded for the strawberries at each price. $d. \$ 4.50$ $\qquad e.\$ 3.25$ $\qquad f.\$ 2.40$ $g.$ Graph $p=5-0.25 q$. Suppose the price and supply of strawberries are related by $p=S(q)=0.25 q$, where $p$ is the price (in dollars) and $q$ is the quantity supplied (in hundreds of quarts) of strawberries. Find the quantity supplied at each price. $h. \$ 0$ $\qquad i.\$ 2$ $\qquad j.\$ 4.50$ $k.$ Graph $p=0.75 q$ on the same axis used for part $g$. $l.$ Find the equilibrium quantity and the equilibrium price.

The manager of a restaurant found that the cost to produce 100 cups of coffee is 11.02 dollars, while the cost to produce 400 cups is 40.12 dollars. Assume the cost C(x) is a linear function of x, the number of cups produced.

Find the marginal cost of the 1001st cup.

A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting) at $55,000, and variable costs (printing, paper, binding, shipping) at$1.60 for each book produced. If the book is sold to distributors for $11 each, how many must be produced and sold for the publisher to break even?