Formulate but do not solve the following exercise as a linear programming problem. kane manufacturing has a division that produces two models of fireplace grates, x units of model a and y units of model b. to produce each model a requires 3 lb of cast iron and 8 min of labor. to produce each model b grate requires 5 lb of cast iron and 3 min of labor. the profit for each model a grate is $2.00, and the profit for each model b grate is $1.50. if 800 lb of cast iron and 1200 min of labor are available for the production of grates per day, how many grates of each model should the division produce per day to maximize kane's profits p in dollars?

maximize p = subject to the constraints
cast iron =
labor =
model a =
y = 0

z  - 2*x   -  1.5*y   =  0   maximize

subject to:

3*x  +  5*y   ≤  800

8*x  + 3*y   ≤   1200  

x, y  >  0

Step-by-step explanation:

Formulation:

Kane Manufacturing produce  x  units of model A (fireplace grates)

and  y units of model B

                  quantity   Iron cast lbs    labor (min)   Profit $    

Model  A          x               3                      8                  2

Model  B          y               5                      3                  1.50

We have   800 lbs of iron cast  and 1200 min  of labor available

We need to find out how many units  x  and units y per day to maximiza profit

First constraint   Iron cast lbs     800 lbs

3*x  +  5*y   ≤  800             3*x  +  5*y  +  s₁   =  800

Second constraint  labor    1200 min available

8*x  + 3*y   ≤   1200              8*x  + 3*y           + s₂  =  1200  

Objective function

z  =  2*x  +  1.5*y         to maximize    z  - 2*x   -  1.5*y   =  0  

x > 0   y  >  0

The first table is  ( to apply simplex method )

z         x        y       s₁      s₂       Cte

1        -2       -1.5     0      0          0

0        3         5       1       0        800

0        8         3       0       1       1200

Sample Response: A positive correlation means that as advertising costs increase, sales also increase. If the slope of the trend line was steeper, the sales would increase more for each increase in advertising. Therefore, it would be to the company owner’s benefit for the slope of the trend line to be steeper.

Step-by-step explanation: