Q. 58

58. Manufacturing Trucks Mike’s Toy Truck Company

manufactures two models of toy trucks, a standard model

and a deluxe model. Each standard model requires 2 hours

(hour) for painting and 3 hour for detail work; each deluxe

model requires 3 hour for painting and 4 hour for detail work.

Two painters and three detail workers are employed by the

company, and each works 40 hour per week.

(a) Using x to denote the number of standard-model trucks

and y to denote the number of deluxe-model trucks,

write a system of linear inequalities that describes the

possible number of each model of truck that can be

manufactured in a week.

(b) Graph the system and label the corner points.

Verified

Answer

(a) the inequalities $\{\begin{cases} x \geq 0 \\ y \geq 0 \\ 2 x + 3 y \leq 80 \\ 3 x + 4 y \leq 120 \end{cases}$

(b) graph

1step 1. Given information

let us consider, standard model requires 2 hours

(hour) for painting and 3 hour for detail work; each deluxe

model requires 3 hour for painting and 4 hour for detail work.

Two painters and three detail workers are employed by the

company, and each works 40 hour per week.

2step 2. Inequality constrains

(a) let x be the standard model and y be the detailed model car

for two workers $2 x + 3 y \leq 2 (40) 2 x + 3 y \leq 80$

for three workers $3 x + 4 y \leq 3 (40) 3 x + 4 y \leq 120$

the time never be zero so $x \geq 0 & y \geq 0$

$\{\begin{cases} x \geq 0 \\ y \geq 0 \\ 2 x + 3 y \leq 80 \\ 3 x + 4 y \leq 120 \end{cases}$

3step 3. Graph with inequalities