$4$The following questions involve analyzing a manufacturing process with multiple work$-$

stations, each with specific processing times, to determine the bottleneck capacity and

calculate the maximum daily profit. Each question provides details about the worksta$-$

tions, operating time, profit per unit, and demand $($assumed sufficient to sell all units

produced$).$ Use the following formulas:

Capacity $($units$/$day$)$: C$=("$ Avallable Time $")/("$ Procossing Time per Unit $")$

Available Time is given in minutes$/$day

C is rounded down to the nearest integer

Bottleneck Capacity: Lowest capacity determines output

Daily Output: Bottleneck capacity $($units$/$day$)$

Daily Profit: P$=$ Daily Output xx Profit per Unit

For each question, determine the bottleneck workstation's capacity and calculate the

maximum daily profit $($in dollars$).$ Provide only the numerical value of the maximum

daily profit.

Question $1$

A toy manufacturing process has four workstations: Assembly, Painting, Drying, and

Packaging. Each workstation operates for $480$ minutes per day. The profit per unit is $$5.$

Question $2$

A furniture production line includes Cutting, Shaping, Sanding, and Finishing. The daily

operating time is $720$ minutes, with a profit of $$12$ per unit.

Question $3$

A bottle manufacturing process involves Melting, Molding, Cooling, and Labeling, oper$-$

ating for $600$ minutes per day. Profit per unit is $$3.$

Question $4$

A circuit board production has Solder Paste Application, Component Placement, Reflow

Soldering, and Inspection. Operating time is $960$ minutes per day, with a profit of $$15$

per unit.

Question $5$

A textile process includes Spinning, Weaving, Dyeing, and Cutting, with $540$ minutes of

daily operation. Profit per unit is $$8.$

Question $6$

A food packaging line has Mixing, Filling, Sealing, and Boxing, operating for $480$ minutes

per day. Profit per unit is $$4.$

Question $7$

A metal fabrication process includes Cutting, Bending, Welding, and Polishing, with $720$

minutes of operation daily. Profit per unit is $$10.$

Question $8$

A glassware production line has Forming, Annealing, Inspecting, and Packing, operating

for $600$ minutes per day. Profit per unit is $$6.$

Question $9$

A paper product process includes Pulping, Pressing, Drying, and Cutting, with $960$

minutes of daily operation. Profit per unit is $$9.$

Question $10$

A ceramic tile production has Mixing, Pressing, Glazing, and Firing, operating for $720$

minutes per day. Profit per unit is $$7.$