CA $2$

Total Marks $-25$

Solve graphically,

$(7$ marks$)$

Maxz$=3x_1+2x_2$

Subject $to$

$2x_1+x_{2}18$

$2x_1+3x_{2}42$

$3x_1+x_{2}24$

$x_1,x_{2}0$

Two tailors A and B earn Rs$.300$ and Rs$.400$ per day respectively. A can stitch $6$ shirts and $4$ pairs of trousers while B can stitch $4$pairs shirts and trousers per day. To find how many days should each of them work and if it is desired to produce at least $60$ shirts and $32$ pairs of trousers at a minimum labor cost, formulate this as an L$.$P$.$P$.$

$(5$ marks$)$

Solve the following LPP graphically

$(7$ marks$)$

MaxZ$=4x+5y$

Subject $to$

$x+y203x$

$+4y72$

$x,y0$

A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least $8$ units of vitamin A and $10$ units of vitamin C$.$ Food'I' contains $2$ units $\frac{?}{kg}$ of vitamin A and $1$ unit $\frac{?}{kg}$ of vitamin C$.$ Food $\text{'}$II$\text{'}$ contains $1$uni$\frac{t}{k}g$ of vitamin A and $2$unit$\frac{s}{k}g$ of vitamin C$.$ It costs Rs $50$ per kg to purchase Food $\text{'}$I$\text{'}$ and Rs $70$ per kg to purchase Food $\text{'}$II$\text{'}.$

Formulate this problem as a linear programmingproblem to minimise the cost of such a mixture.

$(6$ marks$)$