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Melanie King is the manager for the Learning Loft Day Care Center. The center offers all day service for the preschool children for $18 per day and after...

School only service for $6 per day. Fire codes permit only 50 people in the building at one time. State law dictates that a child care worker can be responsible for a maximum of 3 preschool children or 5 school-age children at one time. Ms. King had ten child care workers available to work at the center during the week. How many children of each age group should Ms. King accept to maximize the daily income of the center?
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1 Answer

I developed the following equation: Target equation: A*18+B*18+C*6+D*6 =; A= preschool children B= 5 school age children; C preschool children after school; D 5 school age children after school. The constraints are: A+B<50; C+D<50; (A/3) +(B/5) =10; (C/3) + (D/5) = 10.
I ran the solver of excel to maximize the Target equation result and I obtained:
Worksheet: [Book1]Sheet1
Report Created: 5/15/2014 11:40:16 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied. A=0; B=50; C=0; D=50 Maximum income 1200 a day
Solver Engine
Solver Options
Objective Cell (Max)
Cell Name Original Value Final Value
$D$4 48 1200
Variable Cells
Cell Name Original Value Final Value Integer
$D$5 A 1 0 Contin
$D$6 B 1 50 Contin
$D$7 C 1 0 Contin
$D$8 D 1 50 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$D$10 50 $D$10<=50 Binding 0
$D$11 10 $D$11=10 Binding 0
$D$12 10 $D$12=10 Binding 0
$D$9 50 $D$9<=50 Binding 0