Sporting Equipment, Inc. makes two types of balls: Soccer balls and Cork balls. The making of each soccer ball and cork ball requires 3 hours and 4 hours of production time, respectively. For the next month, the total production hours of 500 are available. Also, the combined production quantity for these two balls must be at least 150 units. The objective for this linear programming model is to fulfil the given production requirements at a minimum cost. The production cost for each Soccer ball is S7 and each Cork ball is $9.
1. Formulate the problem, using the following decision variables:
S = number of Soccer balls manufactured
C = number of Cork balls manufactured
2. The objective function is:
A. Maximize 9S + 7C
B. Minimize 7S + 9C
C. Minimize 9S + 7C
D. Maximize 7S + 9C
3. The constraint equation for the production hours is:
A. 3S + 4C >= 500
B. 4S + 3C <= 500
C. 4S + 3C <= 500
D. 3S + 4C <= 500
4. The constraint equation for the combined production quantity is:
A. S + C <= 150
B. S + C >= 150
C. S + C = 150
D. S + C =/150
5. If the company produces 100 soccer balls and 50 cork balls, the cost of production is:
a. $1250 b. $1350 c. $1150 d. $2000

2) B). Minimize 7S + 9C

3) D) . 3S + 4C ≤ 500

4) B). S + C ≥ 150

5) C) $1150

Step-by-step explanation:

The company makes two types of balls, the balls and their costs are written below:

Soccer ball, S = $7

Cork ball, C = $9

Production time of each ball:

Soccer ball = 3 hours

Cork balls = 4 hours

2) To find the objective function.

Since the cost of each soccer ball is $7 and S balls are produced, the total cost of soccer balls is 7S.

Similarly, the cost of each cork ball is $9 and C balls are produced, total cost is 9C.

The objective function maximize profits and minimizes losses. Here, the objective for this linear programming model is to fulfil the given production requirements at a minimum cost.

Therefore the objective function here is: Minimize 7S+9C

3)The constraint equation for the production hours.

To produce one soccer ball, 3 hours are needed, i.e 3S, to produce one Cork ball 4 hours are needed, i.e 4C.

Since we are given a maximum productin time of 500 hours, the constraint equation for the production hours would be:

3S + 4C ≤ 500

4) Since we are told the combined production quantity for these two balls must be at least 150 units, the constraint equation for the combined production quantity is:

S + C ≥ 150

5)Since each soccer ball costs $7, 100 soccer balls would cost:

7*100 = $700

Similarly, since each Cork ball costs $9, 50 cork balls would cost:

9*50 = $450

Therefore the total cost of production would be:

$700 + $450 = $1,150

Note: Question number 1 isn't a question, it's an expression.