a company produces two products, a and b. at least 30 units of product a and at least 10 units of product b…

a company produces two products, a and b. at least 30 units of product a and at least 10 units of product b must be produced. the maximum number of units that can be produced per day is 80. product a yields a profit of $15 and product b yields a profit of $8. let a = the number of units of product a and b = the number of units of product b. what objective function can be used to maximize the profit? p = 15 a + 8 b complete the vertices of the feasible region are (70, 10), (30, 10), and (30, 50). to maximize the profit, the company should produce units of product a and units of product b. the maximum profit is $ done
Answer
Answer:
70, 10, 1130
Explanation:
Step1: Recall profit - function evaluation
The profit function is $P = 15a+8b$.
Step2: Evaluate at vertex $(70,10)$
$P_1=15\times70 + 8\times10=1050 + 80=1130$.
Step3: Evaluate at vertex $(30,10)$
$P_2=15\times30+8\times10 = 450+80 = 530$.
Step4: Evaluate at vertex $(30,50)$
$P_3=15\times30+8\times50=450 + 400=850$.
Step5: Compare profit values
Since $1130>850>530$, the company should produce 70 units of product A and 10 units of product B for a maximum profit of $1130$.