A fast food shop plans to employ 8 full-time staff and some part-time staff.Suppose that the daily wages for a full-time staff and a part-time staff are $350 and $250 respectively. In order to control the daily running cost, the total expenditure on wages must not exceed $5000 per day.
(a) At most how many part-time staff can be employed?
(b) Hence, find the total daily wages.
Let x = part - time staff
Total cost for full-time workers =
350 * 8 = 2800
2800 + 250x = 5000
250x = 5000 - 2500
x = 8.8
Since I have not met 4/5'ths of a person we would have to either round up or down. Since the daily wage cannot exceed $5000 we will round down to 8.
Therefore they can hire 8 part time workers and 8 full time workers without exceeding daily wage cap.
Therefore Total cost is: 2800 + 250(8) =4800
$2000 to part time workers
$2800 to full time workers.
EDIT:
Change 250x = 5000 - 2500
to: 250x = 5000 - 2800
To determine the number of part-time staff that can be employed, we need to consider the total daily wages and the constraints on the total expenditure.
(a) To find the maximum number of part-time staff, we need to determine the maximum number of full-time staff and subtract it from the total number of staff. The total daily wages cannot exceed $5000.
Let's assume the number of part-time staff to be "x." We know the wages for full-time staff is $350, and the wages for part-time staff is $250.
The total expenditure on full-time staff per day = $350 × 8 = $2800.
Therefore, the maximum expenditure that can be used for part-time staff = $5000 - $2800 = $2200.
Now, we can calculate the maximum number of part-time staff using the given wage of $250:
Maximum number of part-time staff = Maximum expenditure for part-time staff / Wage per part-time staff
Maximum number of part-time staff = $2200 / $250
Maximum number of part-time staff ≈ 8.8
Since we cannot have a fractional number of staff, the maximum number of part-time staff is 8.
(b) To find the total daily wages, we can calculate the wages for full-time staff and part-time staff separately and then add them.
Total daily wages = (Number of full-time staff × Wage per full-time staff) + (Number of part-time staff × Wage per part-time staff)
Substituting the given values, we get:
Total daily wages = (8 × $350) + (8 × $250)
Total daily wages = $2800 + $2000
Total daily wages = $4800
Therefore, the total daily wages are $4800.