A supplier for the automobile industry manufactures car and truck frames at two different plants. How many hours should each plant be scheduled to operate to exactly fill each of the orders in the table? The production rates (in frames per hour) for each plant are given in the first table (on the left side).

Plant Car Frames Truck Frames

A 6 6

B 7 3

Orders

1 2 3

Car frames 1732 1150 1917

Truck frames 1236 676 1257

Complete the table below:

Orders

1 2 3

Number of hours for plant A ______ ______ ______

Number of hours for plant B ______ ______ _______

• Use the Leontief closed model to solve the linear system and determine the dollar amount each organization pays for a credit. Use a scale factor of s = 100.
• For each organization, calculate the ratio of the number of credits required and cost per credit. What does this information provide?

Provide your solution and recommendations.

Let vectors u and v form a basis in some plane, in each of the following cases determine if the vectors e1 and e2 for a basis in this plane:

a)e1=u+v e2=u-v b)e1=-u+2v e2=3u-6v

substantiate your decision

L= {x^a y^b z^c | c=a+b(mod 2)} .Create a DFA and NFA for the language L. Solution and explanation please..

STATCRUNCH STEPS FOR CONFIDENCE INTERVAL AND HYPOTHESIS TESTING CALCULATIONS (WEEKS 4 AND 5)

Several years​ ago, a government agency reported the default rate​ (the proportion of borrowers who default on their​ loans) on a certain type of loan at

0.045 Set up the null and alternative hypotheses to determine if the default rate this year is greater than 0.045.

Let L be the set of all linear transforms from R3 to R2

(a) Verify that L is a vector space.

(b) Determine the dimension of L and give a basis for L.

For the following functions f and g : f(x, y) = e^ax − (1 − a)lny a > 0 g(x, y, z) = −3x^2 − 3y^2 − 3z^2 + 2xy + 2xz + 2yz

1. Calculate the Hessian matrices of f and g noted Hf (x, y) and Hg(x, y, z)

2. Show that Hg(x, y, z) is define negativly for all (x, y, z) ∈ Dg

3. For what value o a is , Hf (x, y) define positivly for any (x, y) ∈ Df ?

• Encipher each plaintext trigraph code by computing (Plaintext trigraph code)^{Public Key}, dividing the result by the Modulus and taking the remainder.

Okay so the trigraph key is 2723 and the public key is 97 and the modulus is 50657. Literally every calculator i use says the number is too large. I am so confused. These are the numbers what is the problem. Is this the wrong formula the teacher gave us this formula. I am so confused.

Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. The Classic Corvette Owners Association scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms available for convention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically request a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two-night package, or make a Friday night only or Saturday night only reservation. Thus, six types of reservations are possible: convention customers/two-night package; convention customers/Friday night only; convention customers/Saturday night only; regular customers/two-night package; regular customers/Friday night only; and regular customers/Saturday night only.

The cost for each type of reservation is shown here:

The anticipated demand for each type of reservation is as follows:

Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue.

1. Define the decision variables and state the objective function. Round your answers to the nearest whole number.
   

   Let	CT = number of convention two-night rooms
   	CF = number of convention Friday only rooms
   	CS = number of convention Saturday only rooms
   	RT = number of regular two-night rooms
   	RF = number of regular Friday only rooms
   	RS = number of regular Saturday only room

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

2. Formulate a linear programming model for this revenue management application. Round your answers to the nearest whole number. If the constant is "1" it must be entered in the box.
   

   CT

   +

   CF

   +

   CS

   +

   RT

   +

   RF

   +

   RS

   S.T.

   1)	CT
   2)	CF
   3)	CS
   4)	RT
   5)	RF
   6)	RS
   7)	CT	+	CF
   8)	CT	+	CS
   9)	CT	+	CF	+	RT	+	RF
   10)	CT	+	CS	+	RT	+	RS
   11)	CT,	CF,	CS,	RT,	RF,	RS			0

3. What are the optimal allocation and the anticipated total revenue? Round your answers to the nearest whole number.
   

   Variable	Value
   CT
   CF
   CS
   RT
   RF
   RS

   
   Total Revenue = $  
   
4. Suppose that one week before the convention the number of regular customers/Saturday night only rooms that were made available sell out. If another nonconvention customer calls and requests a Saturday night only room, what is the value of accepting this additional reservation? Round your answer to the nearest dollar.
   
   The dual value for constraint 10 shows an added profit of $   if this additional reservation is accepted.

A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution flows out of the tank at a rate of 3 L/min. Set up a DE that governs this situation in terms of the mass of salt in the tank. Solve it.

For each of the properties reflexive, symmetric, antisymmetric, and transitive, carry out the following.

Assume that R and S are nonempty relations on a set A that both have the property. For each of R complement (Rc), R∪S, R∩Sand R−1. determine whether the new relation

1. must also have that property;
2. might have that property, but might not; or
3. cannot have that property.

Any time you answer Statement i or Statement iii, outline a proof. Any time you answer Statement ii, provide two examples: one where the new relation has the property, and one where the new relation does not.

Consider a regular 10-gon in which alternate vertices are painted red and blue. Show that the symmetry group of the painted 10-gon is
isomorphic to D5.

Find the solution of the given initial value problem.

2y''+y'-4y=0 ; y(0)=0 y'(0)=1