Q$7.$ There are $1$ meter iron rods. A customer asks seyvw rods of width $45$ cm$,$ thirteen of width $37$ cm$,$ and eight of width $24$ cm$.$ The the number of standard sized rods used. Write the required model in open form. Find six patterns at least $(15$p$.)$

Q$8.$ You have a bag with $21$ weight capacity. There are $7$ items below. The problem is carrying the items to maximize the benefit. If the third item is selected, then the fifth item will be selected also. If both second and fourth items are selected than seventh item must be selected. Write the mathematical model in open form $(20.)$

Item: $1234567$

Benefit: $5832794$

Weight: $78410464$