Question

A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 110 units of A per day. Both products use one raw material, of which the maximum daily availability is 300 lb. The usage rates of the raw material are 2 lb per unit of A, and 4 lb per unit of B The profit units for A and B are $40 and $90, respectively. Determine the optimal product mix for the company

Answer 1

Answer:A=100 , b=25

Step-by-step explanation:

Let sales of A be x and sales of  B be y

Thus $x\geq 0.8(x+y)$

$x\geq 4y$

Also maximum A available is $110\geq x$

$300\geq 2x+4y$

$150\geq x+2y$

We have find the optimal solution for

z=40x+90y

Optimal solution points

(100,25) z$=40\times 100+90\times 25=6250$

(110,20) z$=40\times 110+90\times 20=6200$

(110,0) z$=40\times 110+90\times 0=4400$

Thus for A=100 and B=25 Optimal solution is obtained