For most efficient use, refrigerator freezer compartments should be fully packed with food. What is the thermochemical basis for this recommendation?

a. There are three nucleotides in each codon, and each of these nucleotides can have one of four different bases. How many possible unique codons are there? b. If DNA had only two types of bases instead of four, how long would codons need to be to specify all 20 amino acids?

Suppose the bfs for an optimal tableau is degenerate, and a nonbasic variable in row 0 has a zero coefficient. Show by example that either of the following cases may hold: Case 1: The LP has more than one optimal solution. Case 2: The LP has a unique optimal solution.

Solve the problem:

Felix Schmid decides to establish a budget. He will spend $\$ 700$ for rent, $\$ 325$ for food, $\$ 420$ for child care, $\$ 182$ for transportation, $\$ 300$ for other expenses, and he will put the remainder in savings. If his monthly take-home pay is $\$ 2025$, find his savings

Using complete sentence, answer the following question.
Medicines are classified into five schedules. Describe the legal basis for categorization.

Under what geometric condition will three distinct points in $\mathbf{R}^3$ not determine a unique plane passing through them? How can this condition be expressed algebraically in terms of the position vectors, $\textbf{r}_1$, $\textbf{r}_2$ , and $\textbf{r}_3$, of the three points?

Determine whether the statement is true or false. If $A$ is an $n\times n$ matrix and there exists an orthonormal basis for $R^n$ consisting of eigenvectors of $A$, then $A$ is symmetric.

Find a basis for the subspace $W$ of the vector space $V$. Then find the dimension of $W$. $V=\mathcal{P}_3$ and

$$W=\{f(x)\in V:f(0)+f'(0)+f''(0)=0\}.$$

Solve the mentioned problem on a cold air-standard basis with specific heats evaluated at $520^{\circ} \mathrm{R}$.

Consider the initial-value problem

$$\begin{aligned} \frac{d y}{d x} &=P(x) y^{2}+Q(x) y \\ y(2) &=5 \end{aligned}$$

where $P(x)$ and $Q(x)$ are both third-degree polynomials in $x .$ Has this problem a unique solution on some interval $|x-2| \leq h$ about $x_{0}=2 ?$ Explain why or why not.

A band teacher has a budget of $50,000 to buy new instruments. He will receive 1 free instrument when he places his order. The number of instruments, y, that he can get is given by$y=$\frac{50,000}{x}$+1$, where x is the price per instrument.

What is the vertical asymptote?

A Michelson interferometer is set up to display constructive interference (a bright central spot in the fringe pattern of Figure 22.21) using light of wavelength $\lambda$. If the wavelength is changed to $\lambda / 2$, does the central spot remain bright, does the central spot become dark, or do the fringes disappear? Explain. Assume the fringes are viewed by a detector sensitive to both wavelengths.

Ace Racket Company manufactures two types of tennis rackets, the Junior and Pro Striker models. The production budget for July for the two rackets is as follows:

$$\begin{array}{lcl} & \text { Junior } & \text { Pro Striker } \\ \hline \text { Production budget } & 1,500 \text { units } & 6,200 \text { units } \end{array} Both rackets are produced in two departments, Forming and Assembly. The direct labor hours required for each racket are estimated as follows:$$

$$\begin{array}{lcc} & \text { Forming Department } & \text { Assembly Department } \\ \hline \text { Junior } & 0.16 \text { hour per unit } & 0.24 \text { hour per unit } \\ \text { Pro Striker } & 0.20 \text { hour per unit } & 0.30 \text { hour per unit } \end{array}$$

$$The direct labor rate for each department is as follows:$$

$$\begin{array}{lr} \text{Forming Department}&\text{\$18.00 per hour}\\ \text{Assembly Department}& \text{\$ 14.00 per hour} \end{array}$$

$$Prepare the direct labor cost budget for July 2016.$$

Connie has a monthly income of $\$ 200$ that she allocates between two goods: meat and potatoes.

a. Suppose meat costs $\$ 4$ per pound and potatoes $\$ 2$ per pound. Draw her budget constraint.

b. Suppose also that her utility function is given by the equation $U(M, P)=2 M+P$. What combination of meat and potatoes should she buy to maximize her utility? (Hint: Meat and potatoes are perfect substitutes.)

c. Connie's supermarket has a special promotion. If she buys 20 pounds of potatoes (at $\$ 2$ per pound), she gets the next 10 pounds for free. This offer applies only to the first 20 pounds she buys. All potatoes in excess of the first 20 pounds (excluding bonus potatoes) are still $2 per pound. Draw her budget constraint.

d. An outbreak of potato rot raises the price of potatoes to$\$4$ per pound. The supermarket ends its promotion. What does her budget constraint look like now? What combination of meat and potatoes maximizes her utility?