Question

A company produces two products A and B, which have profits of $9 and $7. Each unit of product must be processed on two assembly lines where the required production times are a follows:

Other
ANSWERED
asked 2020-12-30

A company produces two products A and B, which have profits of $9 and $7. Each unit of product must be processed on two assembly lines where the required production times are a follows:

\(\begin{array}{|c|c|c|}\hline\text{Product}&\text{Line 1}&\text{Line 2}\\\hline A&12&4\\\hline\text{Total hours}&60&40\\\hline\end{array}\)

a. formulate a linear programming model to determine the optimal product mix that will maximize profit.

b. transform this model into standard form.

c. identify the amount of unused resources(i.e., slack)at each of the graphical extreme points.

d. what would be the effect on the optimal if the production time on line 1 were reduced to 40 hours.

c. What would be the effect on the optimal solution if the profit for product B were increased from $7 to $15? To$20?

 

Answers (1)

2020-12-31

Plot the straight lines 12x+4y=60

Consider (shade) the region between this line and the origin of the graph paper, 4x+8y=40

consider (shade) the region between thisline and the origin of the graph paper

The region common for the two above is the critical region and one of its vertices give the maximum profit.The vertices of the critical region are:

(0, 0) with unused 60 hours ofline 1 and 40 hours of Line 2, NSK (0, 5), with unused 40 hoursof line 1 ,

(4, 3) with no unused resources. as (4, 3) represents 4 units of product A and 3 units of product B which utilizes 12*4+4*3=60 hours of Line 1 and 4*4+8*3=40 hours of Line 2.

and (5,0) with unused 20 hours of Line 2

The profit function is P=9x+7y

P is maximum at (4,3)

In the part (b) of the problem the line (1) will be 12x+4y=40

 
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-05-18
Lightning produces a maximum air temperature on the order of \(\displaystyle{9.3}\times{10}^{{{3}}}{K}\), whereas a nuclear explosion produces a temperature on the order of \(\displaystyle{9.2}\times{10}^{{{6}}}{K}\). Use Wien's displacement law to calculate the wavelength of the thermally-produced photons radiated with greatest intensity by each of these sources. Select the part of the electromagnetic spectrum where you would expect each to radiate most strongly.
(a) lightning
\(\displaystyle\lambda_{{\max}}\approx{n}{m}\)
b) nuclear explosion
\(\displaystyle\lambda_{{\max}}\approx\pm\)
asked 2021-06-19
When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon the attentional blink (AB). A study published in Advances in Cognitive Psychology (July 2013) investigated whether simultaneous or preceding sounds could reduce AB. Twenty subjects were presented a rapid visual stream of symbols and letters on a computer screen and asked to identify the first and second letters (the targets). After several trials, the subject's AB magnitude was measured as the difference between the percentages of first target and second target letters correctly identified. Each subject performed the task under each of three conditions. In the Simultaneous condition, a sound (tone) was presented simultaneously with the second target; in the Alert condition, a sound was presented prior to the coming of the second target; and in the No-Tone condition, no sound was presented with the second target. Scatterplots of AB magnitude for each possible pair of conditions are shown below as well as the least squares line for each. a. Which pair of conditions produces the least squares line with the steepest estimated slope? b. Which pair of conditions produces the least squares line with the largest SSE? c. Which pair of conditions produces the least squares line with the smallest estímate of σ?
asked 2021-05-05
If John, Trey, and Miles want to know how’ | many two-letter secret codes there are that don't have a repeated letter. For example, they want to : count BA and AB, but they don't want to count“ doubles such as ZZ or XX. Jobn says there are 26 + 25 because you don’t want to use the same letter twice; that’s why the second number is 25.
‘Trey says he thinks it should be times, not plus: 26-25, Miles says the number is 26-26 ~ 26 because you need to take away the double letters. Discuss the boys’ ideas, Which answers are correct, which are not, and why? Explain your answers clearly and thoroughly, drawing ‘on this section’s definition of multiptication.. -
asked 2021-03-26
A pair of forces with equal magnitudes, opposite directions,and different lines of action is called a "couple". When acouple acts on a rigid object, the couple produces a torque thatdoes not depend on the location of the axis. The drawing shows acouple acting on a tire wrench, each force being perpendicular tothe wrench. Determine an expression for the torque produced by thecouple when the axis is perpendicular to the tired and passesthrough (a) point A, (b) point B, and (c) point C. Express youranswers in terms of the magnitude F of the force and the length Lof the wrench
asked 2021-03-16
The Moon and Earth are bound together by gravity. If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in sing, find the quantity of charge that would have to be placed on each to produce the required force.
asked 2021-02-25
We will now add support for register-memory ALU operations to the classic five-stage RISC pipeline. To offset this increase in complexity, all memory addressing will be restricted to register indirect (i.e., all addresses are simply a value held in a register; no offset or displacement may be added to the register value). For example, the register-memory instruction add x4, x5, (x1) means add the contents of register x5 to the contents of the memory location with address equal to the value in register x1 and put the sum in register x4. Register-register ALU operations are unchanged. The following items apply to the integer RISC pipeline:
a. List a rearranged order of the five traditional stages of the RISC pipeline that will support register-memory operations implemented exclusively by register indirect addressing.
b. Describe what new forwarding paths are needed for the rearranged pipeline by stating the source, destination, and information transferred on each needed new path.
c. For the reordered stages of the RISC pipeline, what new data hazards are created by this addressing mode? Give an instruction sequence illustrating each new hazard.
d. List all of the ways that the RISC pipeline with register-memory ALU operations can have a different instruction count for a given program than the original RISC pipeline. Give a pair of specific instruction sequences, one for the original pipeline and one for the rearranged pipeline, to illustrate each way.
Hint for (d): Give a pair of instruction sequences where the RISC pipeline has “more” instructions than the reg-mem architecture. Also give a pair of instruction sequences where the RISC pipeline has “fewer” instructions than the reg-mem architecture.
asked 2021-05-09
The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)
where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.
Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.
Part B:
A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.
asked 2021-03-07
This problem is about the equation
dP/dt = kP-H , P(0) = Po,
where k > 0 and H > 0 are constants.
If H = 0, you have dP/dt = kP , which models expontialgrowth. Think of H as a harvesting term, tending to reducethe rate of growth; then there ought to be a value of H big enoughto prevent exponential growth.
Problem: find acondition on H, involving \(\displaystyle{P}_{{0}}\) and k, that will prevent solutions from growing exponentially.
asked 2021-05-16
Consider the curves in the first quadrant that have equationsy=Aexp(7x), where A is a positive constant. Different valuesof A give different curves. The curves form a family,F. Let P=(6,6). Let C be the number of the family Fthat goes through P.
A. Let y=f(x) be the equation of C. Find f(x).
B. Find the slope at P of the tangent to C.
C. A curve D is a perpendicular to C at P. What is the slope of thetangent to D at the point P?
D. Give a formula g(y) for the slope at (x,y) of the member of Fthat goes through (x,y). The formula should not involve A orx.
E. A curve which at each of its points is perpendicular to themember of the family F that goes through that point is called anorthogonal trajectory of F. Each orthogonal trajectory to Fsatisfies the differential equation dy/dx = -1/g(y), where g(y) isthe answer to part D.
Find a function of h(y) such that x=h(y) is the equation of theorthogonal trajectory to F that passes through the point P.
asked 2021-03-28

The homogeneous plate ABCD is subjected to a biaxial loading asshown. It is known that \(\displaystyle\sigma_{{z}}=\sigma_{{o}}\) and that the change in length of the plate in the x direction must be zero, that is \(\displaystyle\epsilon_{{x}}={0}\). Denoting E the modulus of elasticity and by v Poisson's ratio, determine (a) the required magnitude of \(\displaystyle\sigma_{{x}}\), and (b) the ratio \(\displaystyle{\frac{{\sigma_{{o}}}}{{\epsilon_{{z}}}}}\)

You might be interested in

...