Question

A company produces two types of goods a and b, that require gold and silver.Each unit of type a requires 3g of silver and1g of gold while that of b requires 1g of silver and 2g of gold.The company can use atmost 9g of silver and 8g of gold.If each unit of type a bring a profit of rupees 40 and that of type b rupees 50,find the number of units of each type that the company should produce to maximize the profit.Formulate and solve graphically the lpp and find maximum profit in . Com

Answer 1

The company should produce 2 units of type A and 3 units of type B to maximize the profit and the maximum profit will be Rs. 230

Explanation

Suppose, the number of units of type A is $x$ and the number of units of type B is $y$

Each unit of type A requires 3 g of silver and 1 g of gold while that of B requires 1 g of silver and 2 g of gold.

So, the total amount of silver in two types  $=(3x+y)$ g

and the total amount of gold in two types  $=(x+2y)$ g.

The company can use at most 9 g of silver and 8 g of gold. So, the constraints are......

$3x+y \leq 9;\\ \\ x+2y\leq 8;\\ \\ x\geq 0; y\geq 0$

Now,  each unit of type A bring a profit of Rs. 40 and that of type B Rs. 50. So, the profit function will be:  $P= 40x+50y$

If we graph the constraints, then the vertices of the common shaded region will be:  $(0,0), (3,0), (2,3)$ and $(0,4)$  (Please refer to the below attached image for the graph)

For (0, 0) ⇒  $P= 40(0)+50(0)=0$

For (3, 0) ⇒  $P= 40(3)+50(0)=120$

For (2, 3) ⇒  $P= 40(2)+50(3)=80+150=230$

For (0, 4) ⇒  $P= 40(0)+50(4)=200$

So, the profit will be maximum when  $x=2$ and $y=3$

Thus, the company should produce 2 units of type A and 3 units of type B to maximize the profit.

The maximum profit will be  Rs. 230

Answer 2

Answer:

Step-by-step explanation:

Here you can see on pic