A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.a. Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.b. The manufacturer is bound by the following constraints:. Equipment in the factory allows for making at most 450 rear-projection televisions in one month.. Equipment in the factory allows for making at most 200 plasma televisions in one month..The cost to the manufacturer per unit is $600 for the rear-projection televisions and $900 for the plasma televisions. Total monthly costs cannot exceed $360,000.Write a system of three inequalities that models these constraints.c.Graph the system of inequalities in part (b).Use only the first quadrant and its boundary, because x and y must both be nonnegative.d. Evaluate the objective function for total monthly profit at each of the five vertices of the graphed region.[The vertices should occur at (0, 0), (0, 200), (300, 200),(450, 100), and (450, 0).]e. Complete the missing portions of this statement: The television manufacturer will make the greatest profit by manufacturing________ rear-projection televisions each month and_______ plasma televisions each month. The maximum monthly profit is $________ .
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.
a. Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.
b. The manufacturer is bound by the following constraints:
. Equipment in the factory allows for making at most 450 rear-projection televisions in one month.
. Equipment in the factory allows for making at most 200 plasma televisions in one month.
.The cost to the manufacturer per unit is $600 for the rear-projection televisions and $900 for the plasma televisions. Total monthly costs cannot exceed $360,000.
Write a system of three inequalities that models these constraints.
c.Graph the system of inequalities in part (b).Use only the first quadrant and its boundary, because x and y must both be nonnegative.
d. Evaluate the objective function for total monthly profit at each of the five vertices of the graphed region.[The vertices should occur at (0, 0), (0, 200), (300, 200),(450, 100), and (450, 0).]
e. Complete the missing portions of this statement: The television manufacturer will make the greatest profit by manufacturing________ rear-projection televisions each month and_______ plasma televisions each month. The maximum monthly profit is $________ .
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