Question

In: Statistics and Probability

Student Enterprises sells two sizes of wall posters, a large 3- by 4-foot poster and a...

Student Enterprises sells two sizes of wall posters, a large 3- by 4-foot poster and a smaller 2- by 3- foot poster. The profit earned from the sale of each large poster is $3; each smaller poster earns $2. The firm, although profitable, is not large; it consists of one art student, Ahmed, at the University of Punjab. Because of her classroom schedule, Ahmed has the following weekly constraints: (1) up to three large posters can be sold, (2) up to five smaller posters can be sold, (3) up to 10 hours can be spent on posters during the week, with each large poster requiring 2 hours of work and each small one taking 1 hour. With the semester almost over, Ahmed plans on taking a three-month summer vacation to Lahore and doesn?t want to leave any unfinished posters behind. Find the integer optimal solution that will maximize her profit. Please show work and do not use any programs for this answer.

Solutions

Expert Solution

In order to find the optimal solution, we need to create a list of the constraint of the products. The following table sums it up:

Poster Time Max Unit Sold Price per unit
Small 1 5 2
Big 2 3 3
Total 10

Then considering x and y units of small and big posters made, the constraints and the objective equations are the following:

Now the region of selection for this set of constraints is the following;

The region is the intersection of all the three regions ( red, blue and green). Now, the critical points and the value of the objective function is given below:

Critical Points Objective function
(0,0) 0
(5,0) 10
(5,2.5) 17.5
(4,3) 17
(0,3) 9

Observe that since we are required to get a integer solution hence, the optimal solution would be to print 4 small and 3 large posters.


Related Solutions

Student Enterprises sells two sizes of wall posters, a large 3- by 4-foot poster and a...
Student Enterprises sells two sizes of wall posters, a large 3- by 4-foot poster and a smaller 2- by 3- foot poster. The profit earned from the sale of each large poster is $3; each smaller poster earns $2. The firm, although profitable, is not large; it consists of one art student, Ahmed, at the University of Punjab. Because of her classroom schedule, Ahmed has the following weekly constraints: (1) up to three large posters can be sold, (2) up...
3. Karen runs a print shop that makes posters for large companies. It is a very...
3. Karen runs a print shop that makes posters for large companies. It is a very competitive business. The market price is currently $1 per poster. She has fixed costs of $250. Her variable costs are $1,000 for the first thousand posters, $800 for the second thousand, and then $750 for each additional thousand posters. What is her AFC per poster (not per thousand!) if she prints 1,000 posters? 2,000? 10,000? What is her ATC per poster if she prints...
You're considering installing a 4-foot-high by 8-foot-wide picture window in a north-facing wall (no solar gain)...
You're considering installing a 4-foot-high by 8-foot-wide picture window in a north-facing wall (no solar gain) that now has a total R (specific thickness of material) value of 23. As a compromise between initial cost and energy savings, you've chosen a standard double-glazed window with the value of R is 2.0. As a result of installing this window, how much more oil will you burn in a 6-month winter heating season with an average outdoor temperature of 25F and an...
Barely Legal Seafoods, a monopolist selling clam chowder, sells two different bowl sizes, large and small....
Barely Legal Seafoods, a monopolist selling clam chowder, sells two different bowl sizes, large and small. What strategy should he use to extract the most surplus possible out of customers who come in two types, regular and big eaters, when he cannot distinguish between the two types by observation? A.Group of answer choices​Distort the size of the small bowl downward to make it less attractive to the big eaters, allowing him to raise the price of the large bowl. B....
A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid,...
A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid, print, and stripe), and two sleeve lengths (long and short). The accompanying tables give the proportions of shirts sold in the various category combinations. Short-sleeved Pattern Size Pl Pr St S 0.04 0.02 0.05 M 0.08 0.05 0.12 L 0.03 0.07 0.08 Long-sleeved Pattern Size Pl Pr St S 0.03 0.02 0.03 M 0.06 0.11 0.07 L 0.04 0.02 0.08 (a) What is the...
A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid,...
A department store sells sport shirts in three sizes (small, medium, and large), three patterns (plaid, print, and stripe), and two sleeve lengths (long and short). The accompanying tables give the proportions of shirts sold in the various category combinations. Short-sleeved Pattern Size Pl Pr St S 0.04 0.02 0.05 M 0.09 0.05 0.12 L 0.03 0.07 0.08 Long-sleeved Pattern Size Pl Pr St S 0.03 0.02 0.03 M 0.08 0.08 0.07 L 0.04 0.02 0.08 (a) What is the...
Your Fan retails computer fans in two sizes: small and large. The business has provided you...
Your Fan retails computer fans in two sizes: small and large. The business has provided you with the following information for a regular month of trading: Small fans Large fans Selling price ($ per fan) 35 55 Purchase price ($ per fan) 25 35 Delivery cost to customer ($ per fan) 1.0 2.0 Monthly fixed cost ($) 15,000 Average monthly sales volume (units) 1,000 600 Business owners are considering selling computer fans in one size only. Retailing one fan size...
A subject property has 2,800 square feet, 4 bedrooms, 3 baths, a 20,000 square foot lot,...
A subject property has 2,800 square feet, 4 bedrooms, 3 baths, a 20,000 square foot lot, brick exterior, and is in “good” condition. The proposed sale price is $185,000. A comparable property sold for $175,000 three months ago.It has 3 bedrooms, 3.5 baths, 2,500 square feet, a 25,000 square foot lot, frame exterior, and is in “excellent” condition. The following adjustments are applicable: House size:$50 per square foot; Lot size:$1.25 per square foot; Bedrooms:$4,000 each; Half bathroom:$750 each; Brick exterior:$4,500...
Riverbed Enterprises is a large Canadian company traded on the Toronto Stock Exchange. Riverbed purchased two...
Riverbed Enterprises is a large Canadian company traded on the Toronto Stock Exchange. Riverbed purchased two copyrights during 2020. The first copyright was purchased on February 1 for $21,700 and was expected to have a useful life until the end of December, 2022. The second copyright was purchased on July 1 for $126,000 and was expected to have an indefinite useful life. Riverbed's fiscal year-end was December 31. On July 1, 2021, Riverbed paid $5,040 in legal fees to successfully...
3. If you have colonies of two colors and sizes on your LB/amp/ara +pGLO plate, is...
3. If you have colonies of two colors and sizes on your LB/amp/ara +pGLO plate, is there any noticeable pattern in the distribution of these colonies? If so, describe what you see. 4. On which of the four plates would you expect to find wild type E. coli growing? What purpose does this plate serve in the design of this experiment?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT