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 midrange of a data set with values 12, 24, 36, 48, and 60?
+
What is the limit as x approaches infinity of (x^2 + 3x + 4) / (2x + 5)?
+
What is the perimeter of a rectangular garden, given the length is 12 meters and the width is 8 meters?
+
New questions in Mathematics
Let f(x)=||x|−6|+|15−|x|| . Then f(6)+f(15) is equal to:
Let the vectors be u=(-1,0,2) , v=(0,2,-3) , w=(2,2,3) Calculate the following expressions a)<u,w> b) &lt;2u- 5v,3w&gt;
A circle with a 12-inch diameter is folded in half and then folded in half again. What is the area of the resulting shape?
Solve: −3(−2x+23)+12=6(−4x+9)+9.
Determine all solutions to the inequality |2x + 6| − |x + 1| < 6. Write your final answer in interval notation
(-5/6)-(-5/4)
-27=-7u 5(u-3)
The physician orders 15mg of tramadol(liquid). On hand is 30mg/2mL vials. How many mL will the MA administer?
Engineers want to design seats in commercial aircraft so that they are wide enough to fit ​95% of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.2 in. Find P95. That​ is, find the hip breadth for men that separates the smallest ​95% from the largest 5​%.
Use a pattern to prove that (-2)-(-3)=1
9 x² + 2x + 1 = 0
2x2
Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?
Calculate the change in internal energy of a gas that receives 16000 J of heat at constant pressure (1.3 atm) expanding from 0.100 m3 to 0.200 m3. Question 1Answer to. 7050J b. 2125J c. None of the above d. 2828J and. 10295 J
For the numbers below, select a number at random and find the probability that: a. The number is even b. The sum of the number’s digit is even c. The number is greater than 50 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
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.
56 × 12 = 672. How should you adjust this answer 672 to determine 57 × 12? a) The answer increases by 1 b) The answer increases by 57 c) The answer increases by 56 d) The answer increases by 12
Sodium 38.15 38.78 38.5 38.65 38.79 38.89 38.57 38.59 38.59 38.8 38.63 38.43 38.56 38.46 38.79 38.42 38.74 39.12 38.5 38.42 38.57 38.37 38.71 38.71 38.4 38.56 38.39 38.34 39.04 38.8 A supplier of bottled mineral water claims that his supply of water has an average sodium content of 36.6 mg/L. The boxplot below is of the sodium contents levels taken from a random sample of 30 bottles. With this data investigate the claim using SPSS to apply the appropriate test. Download the data and transfer it into SPSS. Check that your data transfer has been successful by obtaining the Std. Error of the mean for your data which should appear in SPSS output as 0.03900.. If you do not have this exact value, then you may have not transferred your data from the Excel file to SPSS correctly. Do not continue with the test until your value agrees as otherwise you may not have correct answers. Unless otherwise directed you should report all numeric values to the accuracy displayed in the SPSS output that is supplied when your data has been transferred correctly. In the following questions, all statistical tests should be carried out at the 0.05 significance level. Sample mean and median Complete the following concerning the mean and median of the data. mean =  mg/L 95% CI:  to  mg/L Based upon the 95% confidence interval, is it plausible that the average sodium content is 36.9 mg/L?      median:  mg/L The median value is      36.9 mg/L. Skewness Complete the following concerning the skewness of the data. Skewness statistic =        Std. Error =  The absolute value of the skewness statistic     less than 2 x Std. Error Therefore the data can be considered to come from a population that is      . Normality test Complete the following summary concerning the formal testing of the normality of the data. H0: The data come from a population that     normal H1: The data come from a population that     normal Application of the Shapiro-Wilk test indicated that the normality assumption     reasonable for sodium content (S-W(  )=  , p=   ). Main test Using the guidelines you have been taught that consider sample size, skewness and normality, choose and report the appropriate main test from the following ( Appropriate ONE ) You have selected that you wish to report the one-sample t-test. H0: The mean sodium content     equal to 36.9 mg/L H1: The mean sodium content     equal to 36.9 mg/L Application of the one-sample t-test indicated that the mean is      36.9 mg/L (t(  ) =  , p =   ). You have selected that you wish to report the Wilcoxon signed rank test. H0: The median sodium content     equal to 36.9 mg/L H1: The median sodium content     equal to 36.9 mg/L Application of the Wilcoxon signed rank test indicated that the median is      36.9 mg/L (z =  , N =  , p =   ).
The supply of a good registers periodic increases. With each increase in the offer, the total receipts of the bidders increase. Indicate the correct statement: a) demand is elastic b) demand is inelastic c) supply is inelastic d) supply has unit elasticity.
A gas is leaking at 3.5ft3/min in a room of 2.9m by 6.9ft by 15.7m. How long would it take (in seconds) for 22% of the room to reach the LFL, if the gas has a LFL of 2.51%?

You might be interested in