An ice cream supplier has two machines that produce vanilla and chocolate ice cream. To meet one of its contractual obligations, the company must produce at least 9 gallons of vanilla ice cream and 15 gallons of chocolate ice cream per day. One machine makes 6 gallons of vanilla and 3 gallons of chocolate ice cream per hour. The second machine makes 1 gallons of vanilla and 4 gallons of chocolate ice cream per hour. It costs $28 per hour to run machine 1 and $22 per hour to run machine 2. How many hours should each machine be operated to fulfill the contract at the least expense?
A)Machine 1 for 9 hours and machine 2 for no hours.
B)Machine 1 for 3 hours and machine 2 for 1 hour.
C)Machine 1 for 1 hour and machine 2 for 3 hours.
D)Machine 1 for no hours and machine 2 for 1 hour.
E)Machine 1 for no hours and machine 2 for 3 hours.

Question

Quizplus · Accepted Answer

Let's consider the minimum number of hours each machine needs to operate to meet the contractual obligations:
Machine 1: $9 	ext{ gallons} / 6 	ext{ gallons per hour} = 1.5 	ext{ hours}$
Machine 2: $15 	ext{ gallons} / 4 	ext{ gallons per hour} = 3.75 \approx 4 	ext{ hours}$
Since we cannot operate a machine for a fractional number of hours, we round up to 2 hours and 4 hours for machines 1 and 2, respectively.
The total cost of operating the machines for these minimum hours is:
$2 	ext{ hours} \cdot $28 per hour$ + 4 	ext{ hours} \cdot $22 per hour$ = $56 + $88 = $144
Now, let's consider each choice and calculate its cost:
A) $9 	ext{ hours} \cdot $28 per hour$ + 0 	ext{ hours} \cdot $22 per hour$ = $252
B) $3 	ext{ hours} \cdot $28 per hour$ + 1 	ext{ hour} \cdot $22 per hour$ = $106
C) $1 	ext{ hour} \cdot $28 per hour$ + 3 	ext{ hours} \cdot $22 per hour$ = $94$
D) $0 	ext{ hours} \cdot $28 per hour$ + 1 	ext{ hour} \cdot $22 per hour$ = $22$
E) $0 	ext{ hours} \cdot $28 per hour$ + 3 	ext{ hours} \cdot $22 per hour$ = $66$
Therefore, the least expensive option is to operate machine 1 for 1 hour and machine 2 for 3 hours (choice C).

An Ice Cream Supplier Has Two Machines That Produce Vanilla