10. A company involved in the assembly and distribution of printers in concerned with two types – laser and inkjet. Assembly of each laser printer takes 2 hours, while each inkjet printer takes 1 hour to assemble, and the staff can provide a total of 40 person-hours of assembly time per day. In addition, warehouse space must be available for the assembly and distribution of the printers, for each laser printer and for each inkjet printer; the company has a total of of storage space available for assembled printers each day. Laser printers can be sold for a profit of Rs.30 per unit and inkjet printers earn a profit of Rs.25 each, but the market in which the company is operating can absorb a maximum of 12 laser printers per day. (There is no such limitation on the market for inkjet printers). Find the number of each type of printer the company should assemble and distribute in order to maximize daily profit.

Question

10. A company involved in the assembly and distribution of printers in concerned with two types – laser and inkjet. Assembly of each laser printer takes 2 hours, while each inkjet printer takes 1 hour to assemble, and the staff can provide a total of 40 person-hours of assembly time per day. In addition, warehouse space must be available for the assembly and distribution of the printers, for each laser printer and for each inkjet printer; the company has a total of of storage space available for assembled printers each day. Laser printers can be sold for a profit of Rs.30 per unit and inkjet printers earn a profit of Rs.25 each, but the market in which the company is operating can absorb a maximum of 12 laser printers per day. (There is no such limitation on the market for inkjet printers). Find the number of each type of printer the company should assemble and distribute in order to maximize daily profit.

Answer 1

x=laser

y=inkjet

maximize p=30x+25y subject to
2x+y <= 40
??? for storage
x <= 12

can't proceed until we know about storage space limitations

Answer 2

To solve this problem, we can use linear programming to find the number of each type of printer that the company should assemble and distribute in order to maximize daily profit.

Let's define the variables:
x = number of laser printers to assemble and distribute
y = number of inkjet printers to assemble and distribute

We need to maximize the daily profit, which is given by the following objective function:
Profit = 30x + 25y

Now, let's set up the constraints based on the given information:
1. Assembly time constraint: The total assembly time available per day is 40 person-hours.
2x + y <= 40

2. Warehouse space constraint: The total storage space available for assembled printers per day is .
x + y <=

3. Market limitation for laser printers: The market can absorb a maximum of 12 laser printers per day.
x <= 12

4. Non-negativity constraint: The number of printers cannot be negative.
x >= 0
y >= 0

Now, let's solve this linear programming problem using any optimization method (such as the Simplex method or graphical method) to find the optimal values of x and y that maximize the daily profit.

After solving the linear programming problem, we will have the optimal values of x and y, which will give us the number of each type of printer the company should assemble and distribute in order to maximize daily profit.