A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Each machine is available for a maximum of 6 hours per day. The profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5. We want to maximize the profit. Let x and y toys of type A and type B respectively be manufactured in a day. What is the objective function for this linear programming problem?

7.5x + 5y

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2x+y -60

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2x+y<60

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2x+3y-120

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Solution

The correct option is A
7.5x + 5y

In a linear programming problem, the function we try to maximize or minimize subject to certain constraints is called objective function. In this question we want to maximize profit. The function or expression which represent profit is our objective function. We are given x and y toys of type A and type B respectively are manufactured in a day. Multiplying and adding the corresponding profit per toy will give us the profit. The profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5. So the profit will be 7.5x + 5y. This is the objective function.

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A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Each machine is available for a maximum of 6 hours per day. The profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5. We want to maximize the profit. Let x and y toys of type A and type B respectively be manufactured in a day. What is the objective function for this linear programming problem?

A manufacturer make two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below.
$\begin{matrix} T y p e s & M a c h i n e s I & I I & I I I A & 12 & 18 & 6 B & 6 & 0 & 9 \end{matrix}$
Each machine is available for a maximum of 6 h per day. If the profit on each toy of type A is Rs.7.50 and that the each toy of type B is Rs. 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Type of toys	Machines
Type of toys	I	II	III
A	12	18	6
B	6	0	9

Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

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