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Talja [164]
3 years ago
12

A store has issued two different coupons for its customers to use. One coupon gives customers $20 off their purchase price, and

the other coupon gives customers 20% off of their purchase. The store allows customers to use both coupons and choose which coupon to apply first. For this context, ignore sales tax. Let f be the function that inputs a cost (in dollars) and outputs the cost after applying the "$20 off" coupon, and let g be the function that inputs a cost (in dollars) and outputs the cost after applying the "20% off" coupon. A customer purchases an item for $130 and asks the cashier to apply the "$20 off" coupon first, followed by the "20% off" coupon. What is the cost of the item after the two coupons are applied?
Business
1 answer:
tamaranim1 [39]3 years ago
8 0

Answer:

Price= $88

Explanation:

Giving the following information:

One coupon gives customers $20 off their purchase price, and the other coupon gives customers 20% off of their purchase. A customer purchases an item for $130 and asks the cashier to apply the "$20 off" coupon first, followed by the "20% off" coupon.

Price= (130-f)*(1-g)= (130-20)*(1-0.20)= $88

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3 years ago
The bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for eff
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Answer:

The solution is given below.

Explanation:

It is a practical, complex scheduling problem that can be easily modelled and solved as IP. Note that  part time and full time employees are paid at different rates. So, it is important that the bank operates to provide required service level (indicated by the number of tellers per hour) while  minimizing total cost due to staff salary.

We use x as full time and y as part time staff.

It would help if you construct a table as shown below to better analyze the problem before  attempting to model it. Red shows work hrs of full time staff and green is for part timers. Just follow  their work hour rules.

So, full timers have 3 options:  

(i) start at 9 – work till 1pm, take 1 hr break, then work 2 – 5 pm

(ii) start at 10 – work till 2pm, take 1 hr break, then work 3 – 6 pm

(iii) start at 11 – work till 3pm, take 1 hr break, then work 4 – 7 pm

that’s all… bank closes at 7 pm.

However, part timers don’t have 1 hr break. They work straight 4 hrs and leave. See green cells  above to understand their alternatives.

Now, decision variables should include this work hour information. Here goes their definition. You  must clearly define decision variables in exam, otherwise, the model is meaningless.

X9 = number of full time staff who start at 9 and follow the hour-related rule (no need to specify  more details; those are already undestood)

X10 = number of full time staff who start at 10 and follow the hour-related rule

X11 = number of full time staff who start at 11 and follow the hour-related rule

Y9 = number of part time staff who start at 9 and follow the hour-related rule

Y10 = number of part time staff who start at 10 and follow the hour-related rule

…. This way you define up to Y15.

You must also specify that:

Xi, Yi >=0, integers.

Objective Function:

Minimize Z = 105*(x9 + x10 + x11) + 32* (y9 + y10 + … + y 15)

You will need one “covering” constraint for each working hour. Both full and part-timers can “cover”  the duty of each hour. Look at the color-coded table (above) column-wise. The 9:00-10:00 hour can  be covered only by x9 and y9 staff; next hour by x9, x10, y9, y10 only,… and so on. So, the

constraints are: (attached with image)

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2 years ago
If 95% and 98% confidence intervals were developed to estimate the true cost of an mp3 player with a known population standard d
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8 0
3 years ago
A car rental agency rents 200 cars per day at a rate of 29 dollars per day. For each 1 dollar increase in the daily rate, 5 fewe
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Answer and Explanation:

Given:

Total car = 200

Rate = $29

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Total increase in rate = a

So , Total decrees in car = 5a

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y = 5,800 + 200a - 145a - 5a²

y = 5,800 + 55a - 5a²

y' = dy / da [5,800 + 55a - 5a²]

y' = -10a + 55

in which , y' = 0

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Answer: The deficit is lower when compared to 2010.

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In 2019, the revenue was $3.422 and expenditure was $4.407 which led to a budget deficit was $985. It can be deduced that there has been a reduction in the budget deficit when compared to 2010.

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