MathMaster logo

MathMaster

  1. Home
  2. general
  3. a company receives sales in 20 per book and 18 per calculator the per unit cost to manufacture each book and calculator ar
Question

A company receives sales in $20 per book and $18 per calculator. The per unit cost to manufacture each book and calculator are $5 and 4$ respectively. The monthly (30 day) cost must not exceed $27000 per month. If the manufacturing equipment used by the company takes five minutes to produce a book and 15 minutes to produce a calculator, how many books and calculators should the company produce to maximise profit? Please solve graphically and

238

likes
1189 views

Answer to a math question A company receives sales in $20 per book and $18 per calculator. The per unit cost to manufacture each book and calculator are $5 and 4$ respectively. The monthly (30 day) cost must not exceed $27000 per month. If the manufacturing equipment used by the company takes five minutes to produce a book and 15 minutes to produce a calculator, how many books and calculators should the company produce to maximise profit? Please solve graphically and

Expert avatar
Darrell
4.5
100 Answers
To maximize profit, the company should produce 1,500 books and 2,250 calculators per month. Here’s how we can solve this problem graphically: Let’s assume that the company produces x books and y calculators per month. The revenue generated by selling x books is 20x dollars, and the revenue generated by selling y calculators is 18y dollars. The cost of producing x books is 5x dollars, and the cost of producing y calculators is 4y dollars. The monthly cost must not exceed 27,000 dollars. Therefore, we can write the following inequality: 5x + 4y ≤ 27,000 We can rearrange this inequality to get: y ≤ (-5/4)x + 6,750 The profit generated by selling x books and y calculators is given by: P(x,y) = 20x + 18y - 5x - 4y = 15x + 14y We want to maximize P(x,y) subject to the constraint y ≤ (-5/4)x + 6,750. We can plot the line y = (-5/4)x + 6,750 and shade the region below it. This region represents the feasible set of solutions. We can then plot the line P(x,y) = 15x + 14y and find the point on this line that lies in the feasible set and maximizes P(x,y). This point corresponds to the optimal solution. I’m sorry, but I’m not able to create a graph for you. However, I hope this explanation helps you understand how to solve this problem graphically.

Frequently asked questions (FAQs)
What is the value of \(x\) for which the function \(f(x) = 10^x\) is equal to the function \(g(x) = e^x\)?
+
Math question: What is the probability of rolling a 6 on a fair six-sided die? (P(event) = number of favorable outcomes / total outcomes)
+
What is the period and range of the cosine function, f(x) = cos x?
+
New questions in Mathematics
1 + 1
a ferry travels 1/6 of the distance between two ports in 3/7 hour. the ferry travels at a constant rate. at this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
Jose bought 3/4 of oil and his sister bought 6/8, which of the two bought more oil?
If O(3,-2) is reflected across x = 2. What are the coordinates of O
4x-3y=24 and 5x-2y=9 solve by elimination
-4y-6(2z-4y)-6
Credit title that represents a payment order. This model, which emerged in Brazil, can only be issued in two specific situations: in the purchase and sale of commercial products or in the provision of services. Select the correct alternative: Question 6Answer The. Present value B. Promissory note w. Present value d. Duplicate It is. Bill of exchange
how many arrangement can be made of 4 letters chosen from the 8 letters of the world ABBSOLUTE
Suppose the Golf ball market is perfectly competitive and the functions are known: Q = 120 – 2Px – 2Py 0.2I Q = 2Px 40 Where I = Consumers' income ($200) and Py = Price of Good Y (40) Calculate the equilibrium elasticity: a) 1.6 b) -6 c) 6 d) 0.6
Three squares have a total area of 35.25 𝑐𝑚2 . The larger square has twice the side-length of the middle-sized square. The smaller square has its side length exactly 0.5 cm smaller than the middle-sixed square. Find the side lengths of each of the three squares.
Let v be the set of all ordered pairs of real numbers and consider the scalar addition and multiplication operations defined by: u+v=(x,y)+(s,t)=(x+s+1,y+t -two) au=a.(x,y)=(ax+a-1,ay-2a+2) It is known that this set with the operations defined above is a vector space. A) calculate u+v is au for u=(-2,3),v=(1,-2) and a=2 B) show that (0,0) #0 Suggestion find a vector W such that u+w=u C) who is the vector -u D) show that axiom A4 holds:-u+u=0
Quadratic equation 2X = 15/X + 7
(X+2)(x+3)=4x+18
A multiple choice exam is made up of 10 questions; Each question has 5 options and only one of them is correct. If a person answers at random, what is the probability of answering only 3 good questions?
Solve for B write your answer as a fraction or as a whole number. B-1/7=4
The average undergraduate cost per tuition, fees, room, and board for all institutions last year was $26,025. A random sample of 40 institutions of higher learning this year indicated that the mean tuition, fees, room, and board for the sample was $27,690, and the population standard deviation is $5492. At the 0.05 level of significance, is there sufficient evidence that the cost has increased? (Remember to follow the steps in hypothesis testing)
Find the set of points formed by the expression 𝜋<|𝑧−4+2𝑖|<3𝜋.
Consider the function f(x)=1/2(x+1)^2-3. Use the preceding/following interval method to estimate the instantaneous rate of change at 𝑥 = 1.
How many digits are there in Hindu-Arabic form of numeral 26 × 1011
A plant found at the bottom of a lake doubles in size every 10 days. Yeah It is known that in 300 days it has covered the entire lake, indicate how many days it will take to cover the entire lake four similar plants.

You might be interested in