A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor and brings a profit of $2.50. The football uses 3 ounces of foam and 30 minutes of labor and brings a profit of $2. The manufacturer has available 48 pounds (768 ounces) of foam, and 120 labor-hours a week. Use the simplex method to determine the optimal production schedule so as to maximize profits.

(24, 224 ) i.e. 24 basketball and 224 footballs

Step-by-step explanation:

Basketball :

uses 4 ounces of foam

20 minutes of labor

profit = $2.50

Football :

uses 3 ounces of foam

30 minutes of labor

profit = $2

Manufacturer has :

768 ounces of foam , 120 labor hours per week,

using the simplex method to determine the optimal production schedule so as to maximize profits

lets assume

x = number of basketball

y = number of footballs

maximize = 2.5 x + 2y  from a linear programming problem

attached below is the detailed solution

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°