The operations manager of a plant making cellular telephones has proposed rearranging the production process to be more efficient. She wants to estimate the time to assemble the telephone using the new arrangement. She believes that the population standard deviation is 15 seconds. How large a sample of workers should she take to estimate the mean assembly time to within 2 seconds with 95% confidence?

Argon in a piston-cylinder assembly is compressed isentropically from state 1, where $p_{1}=300 \mathrm{kPa}, T_{1}=37^{\circ} \mathrm{C},$ to state 2, where $p_{2}=450 \mathrm{kPa}.$ Assuming the ideal gas model with k = 1.67, determine (a) $T_2,$ in $^\circ C,$ and (b) the work, in kJ/kg of argon.

Coal is being discharged from a first conveyor belt at the rate of $120 \mathrm{~kg} / \mathrm{s}$. It is received at $A$ by a second belt which discharges it again at $B$. Knowing that $v_1=3 \mathrm{~m} / \mathrm{s}$ and $v_2=4.25 \mathrm{~m} / \mathrm{s}$ and that the second belt assembly and the coal it supports have a total mass of $472 \mathrm{~kg}$, determine the components of the reactions at $C$ and $D$.

Refrigerant $134 \mathrm{a}$ is compressed with no heat transfer in a piston-cylinder assembly from $30 \mathrm{lbf} / \mathrm{in}^2, 20^{\circ} \mathrm{F}$ to $160 \mathrm{lbf} / \mathrm{in}^2$ The mass of refrigerant is $0.04 \mathrm{lb}$. For the refrigerant as the system, $W=-0.56 \mathrm{Btu}$. Kinetic and potential energy effects are few. Find the final temperature, in ${ }^{\circ} \mathrm{F}$.

Five kg of butane $\left(\mathrm{C}_4 \mathrm{H}_{40}\right)$ in a piston-cylinder assembly undergo a process from $p_1=5\ \mathrm{MPa}, T_1=500\ \mathrm{~K}$ to $p_2=$ $3\ \mathrm{MPa}, T_2=450 \mathrm{~K}$ during which the relationship between pressure and specific volume is $p v^n=$ constant. Determine the work, in kJ.

The 50 - $-\mathrm{b}$ weight is falling at $3 \mathrm{ft} / \mathrm{s}$ at the instant it is $2 \mathrm{ft}$ above the spring and post assembly. Determine the maximum stress in the post if the spring has a stiffness of $k=200 \mathrm{kip} / \mathrm{in}$. The post has a diameter of $3 \mathrm{in}$. and a modulus of elasticity of $E=6.80\left(10^3\right)$ ksi. Assume the material will not yield.

Argon in a piston-cylinder assembly is compressed isentropically from state 1 , where $p_1=150\ \mathrm{kPa}, T_1=35^{\circ} \mathrm{C}$. to state 2, where $p_2=300\ \mathrm{kPa}$. Assuming the ideal gas model with $k=1.67$, determine (a) $T_2$, in ${ }^{\circ} \mathrm{C}$, and (b) the work, in $\mathrm{kJ}$ per $\mathrm{kg}$ of argon.

The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours. (a) If 10 assemblies are tested, what is the probability that at least one fails in less than 100 hours? Assume that the assemblies fail independently. (b) If 10 assemblies are tested, what is the probability that all have failed by 800 hours? Assume the assemblies fail independently.

The number of tonnes, n, of wood pulp produced at Al Pac each day is a function of the number of hours, t, the assembly line is in operation that day and is given by $n(t)=550 t-2 t^2$. The cost, $C$, of producing the wood pulp is a function of the number of tonnes produced and is given by $C(n)=7.5 n+1195$.

How many hours was the plant in operation on a day when the total cost of production was $\$ 91555$ ?

Electric guitar kits originally cost d dollars online. You buy the kits on sale for 50 percent of the original price, plus a shipping fee of $4.50 per kit. After painting and assembly, you sell each guitar online for$(1.5 d+4.5)$ dollars. Find and interpret your profit on each guitar sold.

Consider again the choice between outsourcing and in-house assembly of HomeNet analyzed in Table below. Suppose, however, that the upfront cost to set up for in-house production is $\$ 6$ million rather than $\$ 5$ million, and the cost per unit for in-house production is expected to be $\$ 92$ rather than $\$ 95$.

a. Suppose the outside supplier decides to raise its price above $\$ 110$ /unit. At what cost per unit for the outsourced units would Cisco be indifferent between outsourcing and in-house assembly?

b. Alternatively, suppose the cost for outsourcing remains $\$ 110$ /unit, but expected demand increases above $100,000$ units per year. At what level of annual sales, in terms of units sold, would Cisco be indifferent between these two options?

NPV Cost of Outsourced Versus In-House Assembly of HomeNet

$$\small{ \hspace{45mm}\begin{array}{|cccccccc|} \hline\textbf{Year} &\hspace{0.7cm} 0 &\hspace{0.9cm}1 & \hspace{1.cm}2 & \hspace{1cm}3 & \hspace{1cm}4 & \hspace{1.2cm}5\hspace{.41cm}\\ \end{array}} \\ \small{\begin{array}{|llcccccccc|} \hline \textbf{Outsourced Assembly (\$000s)}\\ 1 & \hspace{-40mm}\textbf{EBIT}& && — & (11,000) & (11,000) & (11,000) & (11,000)&—\\ 2 & \hspace{-40mm}\text{Income Tax at 40\\\%} &&& — & 4,400 & 4,400 & 4,400 & 4,400&—\\ \hline 3 & \hspace{-40mm}\textbf{Unlevered Net Income} &&& — & (6,600)& (6,600)& (6,600) & (6,600)&—\\ 4 & \hspace{-40mm}\text{Less: Increases in NWC}&& & — & 1,650 & — & — & —&(1,650)\\ \hline 5 & \hspace{-40mm}\textbf{Free Cash Flow}& && — & (4,950) & (6,600) &(6,600)&(6,600)& (1,650)\\ 6 & \hspace{-40mm}\textbf{NVP at 12\%} &&& 19,510 \\ \hline \end{array}}$$

$$\small{ \hspace{40mm}\begin{array}{|cccccccc|} \hline\textbf{Year}& &\hspace{0.7cm} 0 &\hspace{0.9cm}1 & \hspace{0.9cm}2 & \hspace{0.9cm}3 & \hspace{0.9cm}4 & \hspace{0.5cm}5\hspace{.41cm}\\ \end{array}} \\ \small{\begin{array}{|llcccccccc|} \hline \textbf{In - House Assembly (\$000s)}\\ 7 & \hspace{-38mm}\textbf{EBIT}& && (5,000)& (9,500) & (9,500) & (9,500) & (9,500)&—\\ 8 & \hspace{-38mm}\text{Income Tax at 40\\\%} &&& 2,000 & 3,800 & 3,800 & 3,800 & 3,800&—\\ \hline 9 & \hspace{-38mm}\textbf{Unlevered Net Income} &&& (3,000) & (5,700)& (5,700) & (5,700)&(5,700)&—\\ 10 & \hspace{-37mm}\text{Less: Increases in NWC}&& & — & 633 & — & — & —&(633)\\ \hline 11 & \hspace{-37mm}\textbf{Free Cash Flow}& && (3,000) & (5,067) & (5,700) &(5,700)&(5,700)& (633)\\ 12 & \hspace{-37mm}\textbf{NVP at 12\%} &&& (20,107)\\ \hline \end{array}}$$

The center post $B$ of the assembly has an original length of $124.7 \mathrm{~mm}$, whereas posts $A$ and $C$ have a length of $125 \mathrm{~mm}$. If the caps on the top and bottom can be considered rigid, determine the average normal stress in each post. The posts are made of aluminum and have a cross-sectional area of $400 \mathrm{~mm}^2 . E_{\mathrm{al}}=70 \mathrm{GPa}$.

Argon in a piston-cylinder assembly is compressed from state 1 , where $T_1=300 \mathrm{~K}, V_1=1 \mathrm{~m}^3$, to state 2 , where $T_2=$ $200 \mathrm{~K}$. If the change in specific entropy is $s_2-s_1=-0.27$ $\mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}$, determine the final volume, in $\mathrm{m}^3$. Assume the ideal gas model with $k=1.67$.

A piston/cylinder assembly shown in figure, contains air at $1380 \mathrm{~K}, 15 \mathrm{MPa}$, with $V_1=10 \mathrm{~cm}^3$ and $A_{\mathrm{syl}}=5 \mathrm{~cm}^2$. The piston is released, and just before the piston exits the end of the cylinder, the pressure inside is $200 \mathrm{kPa}$. If the cylinder is insulated, what is its length? How much work is done by the air inside?